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Luana is planning a trip to Rio de Janeiro and wants to buy some gifts for her friends. She visits a local market where she finds beautiful handmade crafts. She buys 5 necklaces at R$15 each, 3 pairs of earrings at R$8 each, and 2 scarves at R$20 each. If she has a 10% discount coupon for her total purchase, how much will she pay in total after the discount is applied?

Let's solve this step by step: 1. Calculate the total cost of the necklaces: Luana buys 5 necklaces at R$15 each. Total cost of necklaces = 5 * R$15 = <<5*15=75>>R$75 2. Calculate the total cost of the earrings: Luana buys 3 pairs of earrings at R$8 each. Total cost of earrings = 3 * R$8 = <<3*8=24>>R$24 3. Calculate the total cost of the scarves: Luana buys 2 scarves at R$20 each. Total cost of scarves = 2 * R$20 = <<2*20=40>>R$40 4. Calculate the total cost of all items before the discount: Total cost = Total cost of necklaces + Total cost of earrings + Total cost of scarves Total cost = R$75 + R$24 + R$40 = <<75+24+40=139>>R$139 5. Apply the 10% discount to the total cost: Discount amount = 10% of R$139 = 0.10 * R$139 = <<0.10*139=13.9>>R$13.90 Total cost after discount = Total cost - Discount amount = R$139 - R$13.90 = <<139-13.9=125.1>>R$125.10 Therefore, Luana will pay R$125.10 after the discount is applied. #### 125.1

Hans is planning a trip to visit his family in Munich, Germany. He wants to put a new carpet in his living room before he leaves. The room is shaped like a rectangle and measures 8 meters by 12 meters. If the carpet costs 15 euros per square meter, how much will Hans have to pay in total for the carpet?

To find the total cost of the carpet, we need to calculate the area of the room first. 1. The room is a rectangle, so we use the formula for the area of a rectangle: Area = length * width. 2. Given the dimensions of the room are 8 meters by 12 meters, we can calculate the area: Area = 8 * 12 = <<8*12=96>>96 square meters. 3. Now, we need to find the total cost of the carpet. The carpet costs 15 euros per square meter. 4. Multiply the area of the room by the cost per square meter to get the total cost: Total Cost = Area * Cost per square meter = 96 * 15 = <<96*15=1440>>1440 euros. Therefore, Hans will have to pay 1440 euros for the carpet. #### 1440

In the Negev Desert, Israel, a wildlife conservation team is building an enclosure for endangered ibexes. The enclosure will be a rectangular area with a fixed perimeter of 240 meters, due to the limited amount of fencing available. To provide ample space for the ibexes to roam, the team wants to maximize the area of the enclosure. If the length of the enclosure must be at least 20 meters more than its width, what should be the dimensions of the enclosure to achieve the maximum area, and what will be the resulting area in square meters?

Let's solve this step by step: 1. Define variables: Let x be the width of the enclosure, and y be its length. 2. Given the length must be at least 20 meters more than the width, we have y ≥ x + 20. 3. The perimeter is fixed at 240 meters, which gives us the equation 2x + 2y = 240. 4. To find the maximum area, we first express y in terms of x from the perimeter equation: y = <<120 - x=120 - x>>120 - x. 5. Substitute y in terms of x into the inequality y ≥ x + 20: 120 - x ≥ x + 20. 6. Solve for x: 2x ≤ 100, so x ≤ 50. 7. Since the width should be as large as possible to maximize area, we take x = 50 meters. 8. Substitute x into y = 120 - x to find y: y = 120 - 50 = <<120 - 50=70>>70 meters. 9. Calculate the area: Area = x * y = 50 * 70 = <<50 * 70=3500>>3500 square meters. Therefore, the dimensions should be 50 meters by 70 meters to achieve the maximum area of 3500 square meters. #### 3500

Ana Luiza is planning a large feijoada for her family's annual Brazilian Independence Day celebration. She wants to serve at least 20% more food than last year, when 45 people attended and they cooked 15 kg of beef and 20 kg of beans. If the recipe requires a ratio of 3 parts beef to 4 parts beans, and each kilogram of beef serves 3 people, how many kilograms of beans should she cook to meet the increased demand and maintain the traditional recipe ratio?

Let's break down the problem step by step: 1. First, we need to determine the total number of people Ana Luiza is planning to serve this year, considering at least a 20% increase from last year's 45 people. To calculate the increase in the number of people: 20% of 45 = <<20/100*45=9>>9 people Total people this year = 45 + 9 = <<45+9=54>>54 people 2. Since each kilogram of beef serves 3 people, we need to find out how many kilograms of beef are required for 54 people. To calculate the amount of beef needed: 54 people / 3 people per kg = <<54/3=18>>18 kg of beef 3. The recipe requires a ratio of 3 parts beef to 4 parts beans. Therefore, for 18 kg of beef, we need to find the corresponding amount of beans to maintain the ratio. To find the amount of beans: 18 kg of beef * (4 parts beans / 3 parts beef) = 18 * 4 / 3 = <<18*4/3=24>>24 kg of beans 4. To ensure we are meeting the increased demand and maintaining the traditional recipe ratio, we should cook 24 kg of beans. #### 24

Min-ju is making hanji, a traditional Korean paper craft, for her school's cultural festival. She has 240 sheets of colored paper and 180 sheets of plain paper. She wants to make two types of hanji designs: a simple design that requires 2 colored sheets and 1 plain sheet, and a complex design that requires 3 colored sheets and 2 plain sheets. If she wants to use all the colored sheets, how many of each design can she make?

Let's solve this step by step: 1. Define variables: Let x be the number of simple designs and y be the number of complex designs. 2. We know that Min-ju has 240 sheets of colored paper and 180 sheets of plain paper. We also know that each simple design requires 2 colored sheets and 1 plain sheet, while each complex design requires 3 colored sheets and 2 plain sheets. 3. Set up equations based on the information given: a) For colored sheets: 2x + 3y = 240 b) For plain sheets: x + 2y ≤ 180 4. Since Min-ju wants to use all the colored sheets, we'll focus on equation (a). We need to find integer solutions for x and y that satisfy this equation. a) One way to solve this is by trying different values for x and finding the corresponding y that makes 2x + 3y equal to 240. For example, if x = 60, then 2*60 + 3y = 240, which simplifies to 120 + 3y = 240, and further simplifies to 3y = 120, so y = <<120/3=40>>40. Checking if this combination works for plain sheets: 60 + 2*40 = 60 + 80 = <<60+80=140>>140, which is less than 180, so it's a valid solution. Therefore, Min-ju can make 60 simple designs and 40 complex designs. #### 60, 40

Fatima is planning a trip from Dubai to Cairo, a distance of 2,150 kilometers. If her flight is delayed by 15%, how many kilometers will she have traveled when she is halfway to her destination, considering the original distance?

Let's solve this step-by-step: 1. First, we need to calculate 15% of the original distance to find out how much the flight is delayed: 15% of 2150 km = <<15/100 * 2150 = 322.5>> km 2. However, the delay is in terms of time, not distance. Since we're interested in the distance traveled when Fatima is halfway to her destination, we do not need to adjust the original distance due to the delay. We simply need to find the halfway point of the original distance: Halfway point = 2150 km / 2 = <<2150 / 2 = 1075>> km 3. Therefore, when Fatima is halfway to her destination, considering the original distance, she will have traveled 1075 kilometers. #### 1075

+ " Natalia is planning a trip from Moscow to Vladivostok, a distance of 9,289 kilometers. She has a budget of 50,000 rubles for fuel and wants to know how much she can spend per kilometer to stay within her budget. If her car consumes an average of 12 liters of fuel per 100 kilometers, and fuel costs an average of 35 rubles per liter, how many rubles can Natalia spend per kilometer on other expenses to stay within her budget?

To find out how many rubles Natalia can spend per kilometer on other expenses, we first need to calculate the total cost of fuel for the trip. 1. Calculate the total liters of fuel needed for the trip: Total distance = 9,289 kilometers Fuel consumption per 100 kilometers = 12 liters Total fuel needed = Total distance / 100 * Fuel consumption per 100 kilometers Total fuel needed = <<9289 / 100 * 12 = 1114.68>> liters 2. Calculate the total cost of fuel for the trip: Fuel cost per liter = 35 rubles Total fuel cost = Total fuel needed * Fuel cost per liter Total fuel cost = <<1114.68 * 35 = 39013.8>> rubles 3. Calculate the remaining budget after subtracting the fuel cost: Total budget = 50,000 rubles Remaining budget = Total budget - Total fuel cost Remaining budget = <<50000 - 39013.8 = 10986.2>> rubles 4. Calculate how many rubles Natalia can spend per kilometer on other expenses: Total distance = 9,289 kilometers Remaining budget per kilometer = Remaining budget / Total distance Remaining budget per kilometer = <<10986.2 / 9289 = 1.18>> rubles per kilometer Therefore, Natalia can spend approximately 1.18 rubles per kilometer on other expenses to stay within her budget. #### 1.18

The chart below shows the average monthly rainfall in four cities in Vietnam: Hanoi, Ho Chi Minh City, Da Nang, and Hoi An. Based on the data, if the total rainfall in Hanoi and Ho Chi Minh City combined for the months of May, June, and July was 540 mm, and the total rainfall for the same period in Da Nang and Hoi An combined was 420 mm, what was the average monthly rainfall in these four cities for those three months?

To find the average monthly rainfall in these four cities for those three months, we need to calculate the total rainfall for all four cities and then divide by the number of months. 1. First, let's find the total rainfall for Hanoi and Ho Chi Minh City combined for the months of May, June, and July, which is given as 540 mm. 2. Then, let's find the total rainfall for Da Nang and Hoi An combined for the same period, which is given as 420 mm. 3. Now, we can find the total rainfall for all four cities for those three months by adding the total rainfall for Hanoi and Ho Chi Minh City to the total rainfall for Da Nang and Hoi An: 540 mm + 420 mm = <<540 + 420 = 960>>960 mm. 4. Finally, to find the average monthly rainfall in these four cities for those three months, we divide the total rainfall by the number of months (3) and by the number of cities (4) but since the cities are already averaged in the given data, we only need to average over the months: 960 mm / 3 = <<960 / 3 = 320>>320 mm. Therefore, the average monthly rainfall in these four cities for those three months was 320 mm. #### 320

Ayşe is building a scale model of the famous Süleymaniye Mosque in Istanbul. She needs to create a rectangular garden around the mosque using 120 meters of fencing. If the length of the garden must be 3 times the width, and she has already used 20 meters of fencing for the mosque's perimeter, how many meters of fencing will she have left over after completing the garden?

Let's solve this step by step: 1. First, we need to determine the dimensions of the garden. Let's denote the width as W and the length as L. We know that L = 3W. 2. The perimeter of the garden is given by P = 2L + 2W. Since Ayşe has already used 20 meters of fencing for the mosque's perimeter, she has 120 - 20 = <<120 - 20 = 100>> meters of fencing left for the garden. 3. We can set up an equation using the perimeter formula and the fact that L = 3W: 100 = 2(3W) + 2W. 4. Simplifying the equation, we get: 100 = 6W + 2W = 8W. 5. Solving for W, we find: W = 100 / 8 = <<100 / 8 = 12.5>> meters. 6. Since L = 3W, we can calculate L: L = 3 * 12.5 = <<3 * 12.5 = 37.5>> meters. 7. Now, we can find the total amount of fencing needed for the garden: 2L + 2W = 2(37.5) + 2(12.5) = <<2 * 37.5 + 2 * 12.5 = 100>> meters. 8. Since Ayşe has 100 meters of fencing available for the garden, she will have 0 meters of fencing left over after completing the garden. #### 0

Akua is making a traditional Nigerian dish, Jollof rice, for a party. She needs to cook for 24 guests, and her recipe serves 8 people. If she has a 75% chance of having all the ingredients for a single batch, and each batch takes 45 minutes to cook, what is the probability that she will have enough ingredients for all 3 batches and be done cooking within 2.5 hours?

To solve this problem, we'll break it down into steps focusing on scaling the recipe, calculating the probability of having enough ingredients, and determining if Akua can complete cooking within the given time frame. 1. First, we need to calculate how many batches of Jollof rice Akua needs to make for 24 guests. Since her recipe serves 8 people, we divide the total number of guests by the number of people the recipe serves: Number of batches = Total guests / Guests per batch = 24 / 8 = <<24/8=3>>3 batches. 2. Next, we calculate the probability that Akua will have enough ingredients for all 3 batches. Given that there's a 75% chance of having all the ingredients for a single batch, and assuming the availability of ingredients for each batch is independent, we raise the probability of having ingredients for one batch to the power of the number of batches: Probability = (Probability per batch)^Number of batches = (75/100)^3 = <<(75/100)^3=0.421875>>0.421875 or 42.1875%. 3. Now, let's determine if Akua can complete cooking within 2.5 hours. Each batch takes 45 minutes to cook, so we multiply the cooking time per batch by the number of batches to get the total cooking time: Total cooking time = Cooking time per batch * Number of batches = 45 minutes * 3 = <<45*3=135>>135 minutes. 4. Convert the total cooking time from minutes to hours to compare it with the 2.5-hour limit: Total cooking time in hours = Total cooking time in minutes / 60 = 135 / 60 = <<135/60=2.25>>2.25 hours. 5. Since the total cooking time of 2.25 hours is less than 2.5 hours, Akua can complete cooking within the given time frame. However, the question asks for the probability that Akua will have enough ingredients for all 3 batches and be done cooking within 2.5 hours. Given that she can complete cooking within the time frame, the probability depends solely on having enough ingredients for all batches, which we calculated as 42.1875%. Therefore, the probability that Akua will have enough ingredients for all 3 batches and be done cooking within 2.5 hours is 42.1875%. #### 42.1875

Léa is the captain of a French soccer team. They are designing a new rectangular soccer field with a length that is 3 meters more than its width. If the width of the field is 25 meters, what is the area of the field in square meters?

Let's break down the problem step by step: 1. First, we need to find the length of the field. We know the width is 25 meters and the length is 3 meters more than the width: Length = Width + 3 = 25 + 3 = <<25+3=28>>28 meters 2. Now that we have the length and width, we can calculate the area of the field using the formula for the area of a rectangle: Area = Length * Width = 28 * 25 = <<28*25=700>>700 square meters Therefore, the area of the field is 700 square meters. #### 700

Kuzma is making a traditional Russian beef stroganoff recipe that serves 4 people and requires a 25% increase in ingredients to make 5 servings. If the original recipe calls for 300 grams of beef strips, how many grams of beef will Kuzma need for 5 servings?

Let's solve this step by step: 1. The original recipe serves 4 people and requires 300 grams of beef strips. 2. To make 5 servings, Kuzma needs to increase the ingredients by 25%. 3. First, let's calculate 25% of 300 grams: 25% of 300g = <<25/100 * 300 = 75>>75 grams 4. Now, we add this increase to the original amount to find the total needed for 5 servings: 300g + 75g = <<300 + 75 = 375>>375 grams Therefore, Kuzma will need 375 grams of beef strips for 5 servings. #### 375

Tomás's abuela gave him $500 to save for college. If he puts it in a savings account that earns a 4% annual interest rate compounded annually, how much money will he have in 5 years?

Let's break this down step by step: 1. First, we need to understand that compound interest is calculated by adding the interest to the principal amount at the end of each year. So, the amount of money Tomás will have in 5 years is the initial amount plus the interest earned each year. 2. The interest rate is 4% per year, compounded annually. This means that the interest is calculated as a percentage of the principal amount and added to the principal at the end of each year. 3. The formula to calculate the amount of money after n years with compound interest is: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial amount), r is the annual interest rate (in decimal), and n is the number of years. 4. Using this formula, we can calculate the amount of money Tomás will have in 5 years: A = 500(1 + 0.04)^5 First, calculate the decimal value inside the parentheses: 1 + 0.04 = <<1 + 0.04 = 1.04>> Then, raise this value to the power of 5: 1.04^5 = <<1.04^5 = 1.216647398950907>> Now, multiply this result by the principal amount: 500 * 1.216647398950907 = <<500 * 1.216647398950907 = 608.3236994754535>> Round this to two decimal places since we're dealing with dollars: 608.32 Therefore, Tomás will have $608.32 in 5 years. #### 608.32

Maya is planning a large Brazilian festival and needs to make a huge batch of brigadeiros, a traditional Brazilian dessert. The recipe for 20 brigadeiros requires 2 cups of milk, 1 cup of sugar, and 1/2 cup of unsweetened cocoa powder. If Maya wants to make 120 brigadeiros and already has 5 cups of milk, how many more cups of milk will she need to buy to have exactly 20% more than required for the scaled-up recipe?

To solve this, let's break it down into steps: 1. First, determine the amount of milk needed for 120 brigadeiros: Since the recipe for 20 brigadeiros requires 2 cups of milk, we need to find how many times to multiply 20 to get 120. 120 / 20 = <<120 / 20 = 6>>6 times So, the amount of milk needed for 120 brigadeiros is 2 cups * 6 = <<2 * 6 = 12>>12 cups. 2. Maya wants to have exactly 20% more milk than required for the scaled-up recipe: 20% of 12 cups = 0.20 * 12 = <<0.20 * 12 = 2.4>>2.4 cups So, she needs a total of 12 cups + 2.4 cups = <<12 + 2.4 = 14.4>>14.4 cups of milk. 3. Maya already has 5 cups of milk: To find out how many more cups she needs, subtract the amount she has from the total needed: 14.4 cups - 5 cups = <<14.4 - 5 = 9.4>>9.4 cups Therefore, Maya needs to buy 9.4 cups of milk to have exactly 20% more than required for the scaled-up recipe. #### 9.4

L'équipe de football de Marseille a gagné 15 matchs avec une moyenne de 2,5 buts par match. Si l'équipe a également perdu 5 matchs avec une moyenne de 1 but par match, combien de buts a-t-elle marqués au total dans la saison ?

Résolvons ce problème étape par étape : 1. L'équipe a gagné 15 matchs avec une moyenne de 2,5 buts par match. Pour trouver le nombre total de buts marqués dans ces matchs, on multiplie le nombre de matchs par la moyenne de buts par match : 15 * 2,5 = <<15*2.5=37.5>>37,5 buts 2. L'équipe a perdu 5 matchs avec une moyenne de 1 but par match. Pour trouver le nombre total de buts marqués dans ces matchs, on multiplie le nombre de matchs par la moyenne de buts par match : 5 * 1 = <<5*1=5>>5 buts 3. Pour trouver le nombre total de buts marqués dans la saison, on additionne les buts marqués dans les matchs gagnés et perdus : 37,5 + 5 = <<37.5+5=42.5>>42,5 buts 4. Puisque l'on ne peut pas marquer une fraction de but, nous pouvons arrondir au nombre entier le plus proche ou considérer que le problème accepte des réponses décimales. Dans ce cas, nous conserverons la valeur décimale pour plus de précision. #### 42.5

Kofi's family is planning a road trip from Lagos to Abuja, which is 750 km away. Their car's fuel efficiency is 12 km per liter of gasoline, and gasoline costs 450 naira per liter. If they want to budget 150,000 naira for fuel, how many liters of gasoline can they afford to buy for the round trip?

To find out how many liters of gasoline Kofi's family can afford to buy for the round trip, let's break down the problem step by step: 1. First, we need to calculate the total distance of the round trip from Lagos to Abuja and back: The distance one way is 750 km, so the round trip distance is: 750 km * 2 = <<750*2=1500>>1500 km 2. Next, we calculate how many liters of gasoline are needed for the round trip based on the car's fuel efficiency: The car travels 12 km per liter, so for 1500 km, the amount of gasoline needed is: 1500 km / 12 km/liter = <<1500/12=125>>125 liters 3. Now, let's determine how many liters of gasoline they can afford with their budget of 150,000 naira: Gasoline costs 450 naira per liter, so the number of liters they can afford is: 150,000 naira / 450 naira/liter = <<150000/450=333.33>>333.33 liters However, we already calculated that they need 125 liters for the trip. Since they can afford more than needed, the amount they can afford to buy for the round trip is actually limited by how much they need, not how much they can afford. Therefore, Kofi's family can afford to buy 125 liters of gasoline for the round trip. #### 125

Hans has been saving money for a new bike and has €120 in his piggy bank. He wants to buy a bike that costs €180. His parents have agreed to give him an allowance of €5 per week for doing chores. However, Hans also spends €2 per week on sweets. If Hans gets a 10% discount on the bike, how many weeks will it take him to have enough money to buy the bike?

Let's break this down step by step: 1. First, calculate the discounted price of the bike: The bike originally costs \u20ac180, and Hans gets a 10% discount. The discount amount is 10% of \u20ac180, which is <<10 * 180 / 100 = 18>>\u20ac18. So, the discounted price is \u20ac180 - \u20ac18 = <<180 - 18 = 162>>\u20ac162. 2. Next, determine how much more money Hans needs to buy the bike: He already has \u20ac120, and the bike costs \u20ac162, so he needs \u20ac162 - \u20ac120 = <<162 - 120 = 42>>\u20ac42 more. 3. Calculate Hans' weekly savings: He earns \u20ac5 per week for doing chores but spends \u20ac2 per week on sweets. His net weekly savings is \u20ac5 - \u20ac2 = <<5 - 2 = 3>>\u20ac3. 4. Finally, find out how many weeks it will take Hans to save enough money to buy the bike: He needs \u20ac42 more and saves \u20ac3 per week. The number of weeks required is \u20ac42 / \u20ac3 = <<42 / 3 = 14>>14 weeks. Therefore, it will take Hans 14 weeks to have enough money to buy the bike. #### 14

Mei, a wildlife conservationist, is studying the population dynamics of pandas in the Sichuan province. She notices that the pandas in a certain reserve are eating a total of 240 kilograms of bamboo shoots per week. The adult pandas eat 15 kilograms each per week, while the cubs eat 5 kilograms each per week. If there are 8 adult pandas in the reserve, how many cubs are there, assuming that only pandas are eating the bamboo shoots?

Let's solve this step-by-step: 1. First, calculate the total amount of bamboo shoots eaten by the adult pandas: 8 adult pandas * 15 kilograms/panda = <<8*15=120>>120 kilograms 2. Since the total consumption is 240 kilograms and the adults eat 120 kilograms, the cubs must eat the remaining amount: 240 kilograms - 120 kilograms = <<240-120=120>>120 kilograms 3. Now, we know that the cubs eat 5 kilograms each per week. To find the number of cubs, we'll divide the total amount eaten by the cubs by the amount each cub eats: 120 kilograms / 5 kilograms/cub = <<120/5=24>>24 cubs Therefore, there are 24 cubs in the reserve. #### 24

While observing the local wildlife, a birdwatcher notes that a certain bird species spends 3/5 of its day foraging for food and 1/4 of its day resting. If the bird is awake for 16 hours a day, how many hours does it spend on other activities?

To find out how many hours the bird spends on other activities, we need to first calculate the total time it spends foraging and resting. Then, we subtract this total from the number of hours the bird is awake to find the time spent on other activities. 1. Calculate the time spent foraging: Time spent foraging = (3/5) * total awake hours Time spent foraging = (3/5) * 16 Time spent foraging = <<3/5 * 16 = 9.6>> hours 2. Calculate the time spent resting: Time spent resting = (1/4) * total awake hours Time spent resting = (1/4) * 16 Time spent resting = <<1/4 * 16 = 4>> hours 3. Calculate the total time spent on foraging and resting: Total time spent on foraging and resting = Time spent foraging + Time spent resting Total time spent on foraging and resting = 9.6 + 4 Total time spent on foraging and resting = <<9.6 + 4 = 13.6>> hours 4. Calculate the time spent on other activities: Time spent on other activities = Total awake hours - Total time spent on foraging and resting Time spent on other activities = 16 - 13.6 Time spent on other activities = <<16 - 13.6 = 2.4>> hours Therefore, the bird spends 2.4 hours on other activities. #### 2.4

Mrs. Cohen, a teacher at an Israeli high school, is preparing for the upcoming math exam. She wants to create a polynomial equation to test her students' understanding. If she has 15 students in her class and she wants each student to solve a different equation of the form ax^2 + bx + c = 0, where a, b, and c are integers, and the sum of the coefficients (a + b + c) equals the student's ID number, what should be the coefficients a, b, and c for the 8th student in the class, assuming the student IDs range from 1 to 15?

To find the coefficients a, b, and c for the 8th student, we need to create an equation where a + b + c equals the student's ID number, which is 8. 1. Since we are looking for a specific set of coefficients (a, b, c) and the requirement is that their sum equals the student ID, we can choose values that satisfy this condition and also make the quadratic equation solvable. For simplicity, let's start with the smallest possible values for a and b, considering a cannot be 0 since it's a quadratic equation. 2. Let's choose a = 1 (as it's the smallest possible value for a quadratic equation to be valid) and see if we can find suitable values for b and c that add up to 8 - 1 = 7. 3. Now, we need to find b and c such that b + c = 7. To keep it simple and ensure we have integer solutions, let's pick b = 2 and c = 5. These values satisfy our condition because 1 + 2 + 5 = <<1+2+5=8>>8. Therefore, the coefficients a, b, and c for the 8th student in the class should be 1, 2, and 5 respectively. #### 125

The Kuznetsov family is planning a trip to the Moscow Zoo. The probability of seeing a lion on a given day is 0.7, and the probability of seeing a tiger is 0.4. If seeing a lion and a tiger are independent events, what is the probability that the family will see both a lion and a tiger during their visit?

To find the probability that the family will see both a lion and a tiger during their visit, we can follow these steps: 1. Understand that since seeing a lion and a tiger are independent events, the probability of seeing both can be calculated by multiplying the probabilities of each event. 2. Identify the given probabilities: The probability of seeing a lion is 0.7, and the probability of seeing a tiger is 0.4. 3. Multiply these probabilities to find the probability of seeing both a lion and a tiger: 0.7 * 0.4 = <<0.7*0.4=0.28>>. Therefore, the probability that the family will see both a lion and a tiger during their visit is 0.28. #### 0.28

Tom Müller is the captain of the German school soccer team. They are planning a trip to the stadium to watch a professional soccer match. The stadium has a rectangular field with a length of 110 meters and a width of 75 meters. If the field is surrounded by a running track that is 5 meters wide on each side, what is the area of the running track?

To find the area of the running track, we need to first calculate the area of the entire field including the track, and then subtract the area of the soccer field itself. Step 1: Calculate the dimensions of the entire field including the track. The length will be the original length plus twice the width of the track (since the track is on both sides), and the width will be the original width plus twice the width of the track. New length = original length + 2 * track width New length = 110 + 2 * 5 New length = 110 + 10 New length = <<110 + 10 = 120>>120 meters New width = original width + 2 * track width New width = 75 + 2 * 5 New width = 75 + 10 New width = <<75 + 10 = 85>>85 meters Step 2: Calculate the area of the entire field including the track. Area of entire field = new length * new width Area of entire field = 120 * 85 Area of entire field = <<120 * 85 = 10200>>10200 square meters Step 3: Calculate the area of the soccer field itself. Area of soccer field = original length * original width Area of soccer field = 110 * 75 Area of soccer field = <<110 * 75 = 8250>>8250 square meters Now, subtract the area of the soccer field from the area of the entire field to find the area of the running track. Area of running track = Area of entire field - Area of soccer field Area of running track = 10200 - 8250 Area of running track = <<10200 - 8250 = 1950>>1950 square meters Therefore, the area of the running track is 1950 square meters. #### 1950

The Nakamura family is planning a traditional Japanese tea ceremony and wants to package a specific blend of green tea leaves for their guests. They have two types of tea leaves: Sencha, which costs ¥500 per kilogram, and Gyokuro, which costs ¥800 per kilogram. The desired blend is a ratio of 3 parts Sencha to 2 parts Gyokuro. If they want to package 5 kilograms of the blend, how much will it cost them in total?

To find the total cost of the tea blend, we need to calculate the amount of each type of tea leaf needed and then multiply by their respective costs. 1. First, determine the total number of parts in the ratio: 3 parts Sencha + 2 parts Gyokuro = <<3+2=5>>5 parts total. 2. Calculate the amount of each type of tea leaf needed for 5 kilograms of the blend: a) Sencha: (3 parts / 5 parts total) * 5 kilograms = <<3/5*5=3>>3 kilograms b) Gyokuro: (2 parts / 5 parts total) * 5 kilograms = <<2/5*5=2>>2 kilograms 3. Calculate the cost of each type of tea leaf needed: a) Sencha: 3 kilograms * \u00a5500 per kilogram = <<3*500=1500>>\u00a51500 b) Gyokuro: 2 kilograms * \u00a5800 per kilogram = <<2*800=1600>>\u00a51600 4. Find the total cost by adding the costs of Sencha and Gyokuro: \u00a51500 + \u00a51600 = <<1500+1600=3100>>\u00a53100 Therefore, the total cost of the tea blend for the Nakamura family will be \u00a53100. #### 3100

The Vietnamese national soccer team is playing in the World Cup. The team's popularity is increasing exponentially, with the number of fans doubling every 3 days. If there are currently 250,000 fans, how many fans will the team have in 21 days?

To solve this problem, we can use the concept of exponential growth. Since the number of fans doubles every 3 days, we can use the formula for exponential growth: N(t) = N0 \* 2^(t/3), where N(t) is the number of fans at time t, N0 is the initial number of fans, and t is the time in days. 1. First, identify the given values: - Initial number of fans (N0) = 250,000 - Time period for doubling = 3 days - Total time (t) = 21 days 2. Next, calculate how many times the number of fans doubles in 21 days: - Number of doublings = Total time / Time period for doubling = 21 / 3 = <<21 / 3 = 7>>7 times 3. Since the number doubles 7 times, we can calculate the final number of fans by multiplying the initial number by 2 raised to the power of 7: - Final number of fans = Initial number of fans * 2^7 - 2^7 = <<2^7 = 128>> 4. Now, calculate the final number of fans: - Final number of fans = 250,000 * 128 = <<250000 * 128 = 32000000>> Therefore, the Vietnamese national soccer team will have 32,000,000 fans in 21 days. #### 32000000

Özge is planning a road trip from Istanbul to Antalya, a distance of 760 km. Her car's fuel efficiency is 12 km/L, and gas costs 7 TRY per liter. If she wants to minimize her fuel cost and has two route options, one that is 50 km longer but has no tolls, and another that is the direct route but includes a 30 TRY toll, which route should she choose to save money?

Let's solve this step by step: 1. First, let's calculate the total fuel consumption for the direct route: Distance = 760 km Fuel efficiency = 12 km/L Fuel consumption for the direct route = Distance / Fuel efficiency = <<760 / 12 = 63.33>>L 2. Next, calculate the fuel cost for the direct route: Fuel cost = Fuel consumption * Gas cost per liter = 63.33 L * 7 TRY/L = <<63.33 * 7 = 443.31>>TRY 3. Then, calculate the total cost for the direct route including the toll: Total cost for the direct route = Fuel cost + Toll = 443.31 TRY + 30 TRY = <<443.31 + 30 = 473.31>>TRY 4. Now, let's calculate the fuel consumption for the longer route: Distance = 760 km + 50 km = 810 km Fuel consumption for the longer route = Distance / Fuel efficiency = <<810 / 12 = 67.5>>L 5. Calculate the fuel cost for the longer route: Fuel cost = Fuel consumption * Gas cost per liter = 67.5 L * 7 TRY/L = <<67.5 * 7 = 472.5>>TRY 6. Since there are no tolls on the longer route, the total cost is the fuel cost: Total cost for the longer route = 472.5 TRY 7. Comparing the total costs: Total cost for the direct route = 473.31 TRY Total cost for the longer route = 472.5 TRY Therefore, Özge should choose the longer route to save money. #### 472.5

At the Hanoi Zoo, the ratio of monkeys to birds is 3:5. If there are 15 monkeys, how many birds are there?

To find the number of birds, we first need to establish the ratio relationship given. The ratio of monkeys to birds is 3:5, indicating that for every 3 monkeys, there are 5 birds. We are told there are 15 monkeys. 1. We can set up a proportion based on the ratio of monkeys to birds: 3/5 = 15/x, where x is the number of birds. 2. To solve for x, we can cross-multiply: 3x = 5 * 15. 3. Perform the multiplication on the right side: 3x = <<5 * 15 = 75>>75. 4. Divide both sides by 3 to solve for x: x = 75 / 3. 5. Calculate the value of x: x = <<75 / 3 = 25>>25. Therefore, there are 25 birds at the Hanoi Zoo. #### 25

Taro is planning a road trip from Tokyo to Osaka, which is 560 kilometers away. If he wants to drive 3/4 of the distance in the morning and the rest in the afternoon, how many kilometers will he drive in the morning?

To find out how many kilometers Taro will drive in the morning, we need to calculate 3/4 of the total distance. 1. The total distance to Osaka is 560 kilometers. 2. We need to find 3/4 of 560: First, multiply 560 by 3: <<560 * 3 = 1680>> Then, divide the result by 4: <<1680 / 4 = 420>> Therefore, Taro will drive 420 kilometers in the morning. #### 420

Léon plays for a French basketball team that earns 3 points for each 3-pointer made, 2 points for each 2-pointer made, and 1 point for each free throw made. In a recent game, Léon scored a total of 30 points. He made 4 more 2-pointers than 3-pointers and attempted 10 free throws, missing only 2. How many 3-pointers did Léon make?

Let's break this down step by step: 1. Léon scored a total of 30 points. 2. He earns 3 points for each 3-pointer, 2 points for each 2-pointer, and 1 point for each free throw. 3. He made 4 more 2-pointers than 3-pointers. Let's call the number of 3-pointers x. Then, the number of 2-pointers is x + 4. 4. He attempted 10 free throws and missed 2, so he made 10 - 2 = <<10-2=8>>8 free throws. 5. Now, let's write an equation for the total points scored: 3x + 2(x + 4) + 8 = 30. 6. Simplifying the equation: 3x + 2x + 8 + 8 = 30, which becomes 5x + 16 = 30. 7. Subtracting 16 from both sides: 5x = <<30-16=14>>14. 8. Dividing by 5: x = <<14/5=2.8>>2.8. However, since we can't have a fraction of a shot, we'll round down to the nearest whole number, as you can't make a fraction of a 3-pointer. Therefore, Léon made 2 3-pointers. #### 2

Maria is making traditional Hispanic paper flowers for a fiesta. She needs 3/4 of a sheet of colored paper for each flower. If she has 6 sheets of paper, how many flowers can she make?

To solve this problem, we'll break it down into steps. 1. First, let's determine how many flowers Maria can make from one sheet of paper. Since she needs 3/4 of a sheet for each flower, we can calculate the number of flowers per sheet by taking the reciprocal of 3/4, which is 4/3. <<4 / 3 = 1.33333333333>> flowers per sheet 2. Since Maria has 6 sheets of paper, we can find the total number of flowers she can make by multiplying the number of flowers per sheet by the total number of sheets: 1.33333333333 flowers per sheet * 6 sheets = <<1.33333333333 * 6 = 8>> flowers Therefore, Maria can make 8 flowers with the paper she has. #### 8

Amit and his friends are planning a road trip from Tel Aviv to Eilat, a distance of 340 kilometers. Their car's fuel efficiency is 14 kilometers per liter, and gas costs 6 shekels per liter. If they want to minimize their fuel cost, how many liters of gas should they buy for the entire trip?

To find the minimum amount of fuel they should buy, we first need to calculate how much fuel the trip will consume. 1. The distance to Eilat is 340 kilometers. 2. Their car's fuel efficiency is 14 kilometers per liter. 3. To find out how many liters of fuel they'll need, we divide the total distance by the fuel efficiency: <<340 / 14 = 24.29>> liters Since they can't buy a fraction of a liter, we round up to the nearest whole number to ensure they have enough fuel for the entire trip. 4. Rounding 24.29 liters up to the nearest whole number gives us 25 liters. Therefore, to minimize their fuel cost, Amit and his friends should buy 25 liters of gas for the entire trip. #### 25

The Ploy family is planning a Songkran water festival party and wants to make a 20% profit on the sale of traditional Thai desserts. They spend 1,200 THB on ingredients to make Khanom Buang (Thai crepes) and Tub Tim Krob (water chestnut dessert). If they sell each Khanom Buang for 80 THB and each Tub Tim Krob for 60 THB, and they sell 50% more Tub Tim Krob than Khanom Buang, how many of each dessert must they sell to achieve their desired profit?

To solve this problem, let's break it down step by step: 1. First, we need to calculate the total cost of the ingredients used to make both desserts. The Ploy family spends 1,200 THB on ingredients. 2. Next, we need to find the selling price for each dessert. Since they want to make a 20% profit on the sale of these desserts, we need to calculate the total selling price that would give them this profit. Let's denote the total selling price as 'x'. The profit is 20% of the cost price. So, the selling price is the cost price plus the profit. Profit = 20% of 1,200 THB = <<20/100 * 1200 = 240>>THB Total selling price = Cost price + Profit = 1,200 THB + 240 THB = <<1200 + 240 = 1440>>THB 3. We know that the Ploy family sells each Khanom Buang for 80 THB and each Tub Tim Krob for 60 THB. They also sell 50% more Tub Tim Krob than Khanom Buang. Let's denote the number of Khanom Buang sold as 'x'. Then, the number of Tub Tim Krob sold is 1.5x (since it's 50% more). 4. The total selling price can be expressed as the sum of the selling prices of both desserts. Total selling price = (Number of Khanom Buang * Price per Khanom Buang) + (Number of Tub Tim Krob * Price per Tub Tim Krob) 1,440 THB = (x * 80 THB) + (1.5x * 60 THB) 5. Simplify the equation: 1,440 THB = 80x + 90x 1,440 THB = 170x Solve for x: x = 1,440 THB / 170 x = <<1440 / 170 = 8.47>> (round down to 8, since we can't sell fractions of desserts) So, they sell 8 Khanom Buang and 1.5 * 8 = 12 Tub Tim Krob. 6. Therefore, the Ploy family must sell 8 Khanom Buang and 12 Tub Tim Krob to achieve their desired profit. #### 20

Ngọc and her family own a popular Vietnamese bakery in Hanoi, specializing in delicious Bánh Cuốn. They need to package 480 spring rolls for a large catering order, using boxes that hold either 12 or 20 rolls. If they want to use as many of the larger boxes as possible, how many of each box size should they use to pack all 480 spring rolls, given that they have only 25 large boxes available?

Let's solve this step by step: 1. First, we need to find out how many large boxes can be used to pack the spring rolls. We have 25 large boxes available, and each can hold 20 rolls. We calculate the maximum number of rolls that can be packed in the large boxes: 25 large boxes * 20 rolls/large box = <<25*20=500>>500 rolls 2. Since we need to pack only 480 rolls, we can use the large boxes for: 480 rolls / 20 rolls/large box = <<480/20=24>>24 large boxes 3. We'll use 24 large boxes to pack: 24 large boxes * 20 rolls/large box = <<24*20=480>>480 rolls However, this calculation would leave no rolls for the smaller boxes, and we are asked to find a combination of both. So, we should adjust our strategy to maximize the use of large boxes without exceeding the total number of rolls. 4. If we use 24 large boxes, we exceed the number of rolls we have, so let's use 23 large boxes instead: 23 large boxes * 20 rolls/large box = <<23*20=460>>460 rolls 5. Now, we have: 480 total rolls - 460 rolls packed in large boxes = <<480-460=20>>20 rolls left 6. These 20 rolls can be packed in the smaller boxes that hold 12 rolls each: 20 rolls / 12 rolls/small box = <<20/12=1.67>>1.67 small boxes Since we can't use a fraction of a box, we round up to the nearest whole number. However, because we cannot have a fraction of a box and we are trying to use as many of the larger boxes as possible, we need to adjust our strategy considering the available options. 7. Upon reviewing, since we can't fit 20 rolls into a whole number of small boxes without wasting space, and we have already determined the maximum efficient use of the large boxes, we see that using 23 large boxes and adjusting the remainder to fit into small boxes doesn't perfectly optimize for the total of 480 rolls without considering partial boxes or altering the distribution strategy. The most straightforward approach given the constraints is to use the large boxes to their maximum efficient capacity and then use small boxes, but since we can't fit the remaining rolls perfectly into small boxes without exceeding the total, we reconsider our distribution to ensure we're meeting the total requirement of 480 rolls exactly. Given the constraints and the need for whole numbers of boxes, let's correct the distribution strategy focusing on using as many large boxes as possible while ensuring we can accommodate the exact number of rolls with the combination of box sizes available: - If we use 24 large boxes, we exceed the number of rolls we have. So, we use 23 large boxes: 23 large boxes * 20 rolls/large box = <<23*20=460>>460 rolls - This leaves us with 20 rolls, but we need to reconsider how to pack these to meet the exact requirement without exceeding or going under, given the box sizes. Since we can't perfectly fit the remaining rolls into the small boxes as initially calculated due to the fractional result, we reassess our distribution strategy for optimization and exact fit. Given the misstep in calculation towards the end, let's correct and simplify the approach focusing on the original goal of maximizing the use of large boxes and then utilizing small boxes for the remainder, with an emphasis on reaching the total of 480 rolls exactly without exceeding or falling short: 1. Maximize the use of large boxes without exceeding 480 rolls: - 24 large boxes would be too many because 24 * 20 = <<24*20=480>>480, which exactly meets our needs but doesn't allow for any small boxes as initially thought. However, this calculation shows we can indeed meet the requirement exactly with large boxes alone, which contradicts the need for a combination but aligns with maximizing the use of large boxes. 2. Correct the oversight and align with the goal: - The initial goal was to use as many large boxes as possible and then use small boxes. Since we found that 24 large boxes exactly meet the requirement, we have efficiently maximized the use of large boxes. Therefore, the bakery should use 24 large boxes to pack 480 rolls, as this maximizes the use of large boxes and meets the total requirement exactly without the need for additional small boxes under the given constraints and optimization goal. #### 24

Maya and Leila are planning a road trip from Toronto to Vancouver. If they drive at an average speed of 100 km/h for 4 hours a day, and the distance between Toronto and Vancouver is 4300 km, how many days will it take them to complete their trip if they take a 2-day break in Winnipeg, which is 1/3 of the way from Toronto to Vancouver?

To solve this problem, we'll break it down into steps: 1. First, calculate the total driving distance from Toronto to Vancouver without the break: Total distance = 4300 km 2. Since they take a break in Winnipeg, which is 1/3 of the way, we need to find the distance from Toronto to Winnipeg: Distance to Winnipeg = 1/3 * Total distance = <<1/3 * 4300 = 1433.33>> km 3. The remaining distance after the break is the total distance minus the distance to Winnipeg: Remaining distance = Total distance - Distance to Winnipeg = <<4300 - 1433.33 = 2866.67>> km 4. Since they drive at an average speed of 100 km/h for 4 hours a day, we calculate the daily distance covered: Daily distance = Speed * Time = 100 km/h * 4 h = <<100 * 4 = 400>> km/day 5. Now, we need to find out how many days it takes to cover the remaining distance after the break: Days for remaining distance = Remaining distance / Daily distance = <<2866.67 / 400 = 7.166675>> days 6. Since they can't drive a fraction of a day, we round up to the nearest whole number. However, the problem specifically asks for the total number of days including the break, so we must add the 2-day break and the days driven before the break. First, calculate the days driven before the break: Days to Winnipeg = Distance to Winnipeg / Daily distance = <<1433.33 / 400 = 3.583325>> days 7. Round the days driven before the break up to the nearest whole number since you cannot drive a fraction of a day: Days to Winnipeg = 4 days 8. Add the days driven before the break, the break itself, and the days for the remaining distance after rounding up to the nearest whole number for the post-break segment: Total days = Days to Winnipeg + 2-day break + Rounded days for remaining distance = 4 + 2 + 8 = <<4 + 2 + 8 = 14>> days Therefore, it will take Maya and Leila 14 days to complete their trip. #### 14

Tunde is playing a game of ring toss at the annual Ibadan carnival. He has to toss a ring onto a pole from 5 meters away. If the probability of getting the ring on the pole from that distance is 0.2, and he gets 3 chances to toss the ring, what is the probability that he will successfully get the ring on the pole at least once?

To find the probability that Tunde will successfully get the ring on the pole at least once, we need to first find the probability that he will not get the ring on the pole in any of the 3 chances and then subtract that probability from 1. The probability of not getting the ring on the pole in a single toss is 1 - 0.2 = <<1-0.2=0.8>>. Since Tunde gets 3 chances, the probability of not getting the ring on the pole in any of the 3 chances is 0.8 * 0.8 * 0.8 = <<0.8*0.8*0.8=0.512>>. Now, to find the probability that he will get the ring on the pole at least once, we subtract the probability of not getting the ring on the pole in any of the 3 chances from 1: 1 - 0.512 = <<1-0.512=0.488>>. Therefore, the probability that Tunde will successfully get the ring on the pole at least once is 0.488. #### 0.488

Gal is planning a trip from Tel Aviv to New York. She invests 5,000 shekels in a savings account with a 4% annual interest rate compounded annually. If she invests the money for 3 years, how much will she have in total to spend on her trip?

Let's solve this step by step: 1. First, we need to calculate the interest earned each year: The formula for compound interest is A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial investment), r is the annual interest rate, and n is the number of years. For this problem, P = 5000 shekels, r = 4% or 0.04, and n = 3 years. 2. Calculate the amount after the first year: A1 = 5000(1 + 0.04)^1 = 5000 * 1.04 = <<5000 * 1.04 = 5200>>5200 shekels 3. Calculate the amount after the second year: A2 = 5200(1 + 0.04)^1 = 5200 * 1.04 = <<5200 * 1.04 = 5408>>5408 shekels 4. Calculate the amount after the third year: A3 = 5408(1 + 0.04)^1 = 5408 * 1.04 = <<5408 * 1.04 = 5624.32>>5624.32 shekels 5. Therefore, after 3 years, Gal will have approximately 5624.32 shekels in her savings account. 6. To find the total amount she can spend on her trip, we simply take the final amount after 3 years. 7. Total = 5624.32 shekels Therefore, Gal will have a total of 5624.32 shekels to spend on her trip. #### 5624.32

Yuna is studying the population of birds in Tokyo's Imperial Palace East Garden. She observes that the number of birds visiting the garden increases by 15% each month from April to July due to the blooming flowers. If there were 200 birds in April, how many birds can Yuna expect to see in July?

Let's break this down step by step: 1. First, we need to calculate the increase in the number of birds from April to May: The number of birds in April is 200. The increase from April to May is 15% of 200: 15% of 200 = <<15/100 * 200 = 30>> So, the number of birds in May is 200 + 30 = <<200 + 30 = 230>> 2. Next, we calculate the increase from May to June: The number of birds in May is 230. The increase from May to June is 15% of 230: 15% of 230 = <<15/100 * 230 = 34.5>> So, the number of birds in June is 230 + 34.5 = <<230 + 34.5 = 264.5>> 3. Lastly, we calculate the increase from June to July: The number of birds in June is 264.5. The increase from June to July is 15% of 264.5: 15% of 264.5 = <<15/100 * 264.5 = 39.675>> So, the number of birds in July is 264.5 + 39.675 = <<264.5 + 39.675 = 304.175>> Rounding to the nearest whole number, Yuna can expect to see approximately 304 birds in July. #### 304

Amira is planning a party for Eid al-Fitr and wants to make sure she has enough dates and baklava for her guests. She expects 25 guests and plans to serve 5 dates and 2 pieces of baklava per guest. If a box of dates contains 50 dates and a tray of baklava contains 30 pieces, how many boxes of dates and trays of baklava should Amira buy to have exactly enough for her guests?

To solve this, let's break it down into steps: 1. Calculate the total number of dates needed: 25 guests * 5 dates per guest = <<25*5=125>>125 dates 2. Determine the number of boxes of dates needed: Since each box contains 50 dates, we divide the total number of dates needed by the number of dates per box: 125 dates / 50 dates per box = <<125/50=2.5>>2.5 boxes Since we can't buy half a box, we need to round up to the nearest whole number to have enough dates. Therefore, Amira needs 3 boxes of dates. 3. Calculate the total number of pieces of baklava needed: 25 guests * 2 pieces of baklava per guest = <<25*2=50>>50 pieces 4. Determine the number of trays of baklava needed: Since each tray contains 30 pieces, we divide the total number of pieces needed by the number of pieces per tray: 50 pieces / 30 pieces per tray = <<50/30=1.6666666666666667>>1.67 trays Again, since we can't buy a fraction of a tray, we need to round up to the nearest whole number. Therefore, Amira needs 2 trays of baklava. 5. To summarize, Amira should buy 3 boxes of dates and 2 trays of baklava for her party. #### 5

Taro is building a traditional Japanese dollhouse that requires 240 square centimeters of specialized washi paper for the walls and 120 square centimeters for the roof. He has three rolls of washi paper: Roll A has 100 square centimeters, Roll B has 150 square centimeters, and Roll C has 200 square centimeters. If Taro uses Roll A and Roll B, how many square centimeters of washi paper will he still need to buy for the dollhouse?

To find out how many square centimeters of washi paper Taro still needs to buy, we first need to calculate the total amount of washi paper required for the dollhouse and then subtract the amount he already has from Rolls A and B. 1. Calculate the total amount of washi paper needed for the dollhouse: Total washi paper needed = washi paper for walls + washi paper for roof Total washi paper needed = 240 + 120 = <<240+120=360>>360 square centimeters 2. Calculate the total amount of washi paper Taro has from Rolls A and B: Total washi paper from Rolls A and B = washi paper in Roll A + washi paper in Roll B Total washi paper from Rolls A and B = 100 + 150 = <<100+150=250>>250 square centimeters 3. Subtract the amount of washi paper Taro has from the total amount needed to find out how much more he needs to buy: Additional washi paper needed = Total washi paper needed - Total washi paper from Rolls A and B Additional washi paper needed = 360 - 250 = <<360-250=110>>110 square centimeters Therefore, Taro needs to buy 110 square centimeters of washi paper for the dollhouse. #### 110

The Lincoln High School basketball team has won 15 out of 20 games this season, with an average score of 75 points per game. If they maintain this win percentage and average score for the next 10 games, and each game requires a $500 fee for transportation and facilities, how much will the school need to budget in total for the next 10 games, assuming a win is worth 3 points and a loss is worth 1 point, and the team earns $200 for every point earned?

To find the total budget needed for the next 10 games, we'll first determine how many games the team is expected to win and lose based on their current win percentage, then calculate the total points they'll earn from these games, the total fees for the games, and finally, the net amount the school needs to budget after accounting for the earnings from the points. 1. Calculate the expected number of wins and losses in the next 10 games: - Current win percentage is 15 wins out of 20 games, which is 15/20 or 75%. - Expected wins in 10 games = 10 games * 75% = <<10*0.75=7.5>>7.5 games. Since you can't win half a game, we'll round this to the nearest whole number, but for the sake of this calculation, we'll consider the points earned from this as a direct proportion. - Expected losses = 10 games - 7.5 games = 2.5 games. 2. Calculate the total points earned from wins and losses: - Each win is worth 3 points, so points from wins = 7.5 wins * 3 points/win = <<7.5*3=22.5>>22.5 points. - Each loss is worth 1 point, so points from losses = 2.5 losses * 1 point/loss = <<2.5*1=2.5>>2.5 points. - Total points = 22.5 points + 2.5 points = <<22.5+2.5=25>>25 points. 3. Calculate the earnings from the points: - The team earns $200 for every point, so total earnings = 25 points * $200/point = $<<25*200=5000>>5000. 4. Calculate the total fees for the next 10 games: - Each game requires a $500 fee, so total fees = 10 games * $500/game = $<<10*500=5000>>5000. 5. Determine the total budget needed: - The total budget needed is the total fees minus the earnings from points, but since the question asks for how much the school needs to budget in total for the next 10 games without explicitly stating to subtract earnings, and given the standard interpretation would be to find the total cost before earnings, we correct our approach to simply calculate the total fees without subtracting earnings. - Total budget needed = $5000. #### 5000

Maria is building a custom model train set and wants to ensure the tracks are long enough to connect her favorite scenery pieces. The train set has three different track sizes: small (5 inches), medium (7 inches), and large (10 inches). If she needs a total length of 190 inches to connect all the scenery and she has already used 5 large tracks, how many small and medium tracks can she combine to achieve the remaining length, given that she prefers to use as many small tracks as possible?

Let's break this down step by step: 1. First, calculate the total length already covered by the large tracks: 5 large tracks * 10 inches/track = <<5*10=50>>50 inches 2. Next, find the remaining length needed: Total length needed - Length covered by large tracks = 190 inches - 50 inches = <<190-50=140>>140 inches 3. Since Maria prefers to use as many small tracks as possible, let's see how many small tracks can fit into the remaining length: Remaining length / Length of a small track = 140 inches / 5 inches = <<140/5=28>>28 small tracks However, we need to check if we can exactly reach the remaining length with these small tracks, or if we need to adjust by adding medium tracks. 4. Calculate the total length covered by 28 small tracks: 28 small tracks * 5 inches/track = <<28*5=140>>140 inches Since this exactly covers the remaining length, Maria does not need any medium tracks. Therefore, Maria can use 28 small tracks and 0 medium tracks to achieve the remaining length. #### 28

The Garcias are planning a family dinner, and they want to share the cost of the meal equally. If 3/4 of the family members have already contributed $15 each and the total cost of the meal is $120, how much will the remaining family members need to pay if there are 8 members in total?

Let's break this down step by step: 1. First, we need to find out how many family members have already contributed. We're told 3/4 of the members have contributed, and there are 8 members in total. So, the number of members who have contributed is 3/4 * 8 = <<3/4*8=6>>6 members. 2. Since each of these 6 members contributed $15, the total amount contributed so far is 6 * $15 = $<<6*15=90>>90. 3. The total cost of the meal is $120, so the remaining amount needed is $120 - $90 = $<<120-90=30>>30. 4. Since there are 8 members in total and 6 have already contributed, the remaining members who need to pay are 8 - 6 = <<8-6=2>>2. 5. To find out how much each of the remaining members needs to pay, we divide the remaining amount by the number of remaining members: $30 / 2 = $<<30/2=15>>15. Therefore, each of the remaining family members needs to pay $15. #### 15

Fatima is making a scale model of the Burj Khalifa for her school project. If the actual height of the Burj Khalifa is 828 meters and Fatima wants her model to be 1/100th of the actual size, how many centimeters tall should her model be?

Let's solve this step by step: 1. First, we need to convert the height of the Burj Khalifa from meters to centimeters because the model's height is required in centimeters. There are 100 centimeters in a meter. 828 meters * 100 centimeters/meter = <<828*100=82800>>82800 centimeters 2. Fatima wants her model to be 1/100th of the actual size. To find the height of the model, we need to calculate 1/100th of the actual height in centimeters. 1/100 * 82800 centimeters = <<82800/100=828>>828 centimeters Therefore, Fatima's model should be 828 centimeters tall. #### 828

In the Pantanal region of Brazil, a wildlife sanctuary has 240 kilograms of food to distribute among three animal enclosures: birds, reptiles, and mammals. The birds require 2 kilograms of food per day, the reptiles need 3 kilograms per day, and the mammals require 5 kilograms per day. If the sanctuary wants to allocate the food such that the birds receive twice as much food as the reptiles and the mammals receive three times as much food as the birds, how many kilograms of food will the mammals receive?

Let's break down the problem step by step: 1. Define variables for the amount of food each group receives: Let's say the birds receive B kilograms of food, the reptiles receive R kilograms, and the mammals receive M kilograms. 2. According to the problem, the birds receive twice as much food as the reptiles, so we can set up the equation: B = 2R. 3. The mammals receive three times as much food as the birds, so we can set up the equation: M = 3B. 4. The birds require 2 kilograms of food per day, the reptiles need 3 kilograms per day, and the mammals require 5 kilograms per day. Since the total amount of food is 240 kilograms, we can set up the equation: 2B + 3R + 5M = 240. 5. Substitute the expressions from steps 2 and 3 into the equation from step 4 to get: 2B + 3(B/2) + 5(3B) = 240. 6. Simplify the equation: 2B + 1.5B + 15B = 240, which gives us 18.5B = 240. 7. Solve for B: B = <<240 / 18.5 = 12.97>> kilograms. Since M = 3B, we can find the amount of food the mammals receive: M = 3 * 12.97 = <<3 * 12.97 = 38.91>> kilograms. Therefore, the mammals will receive approximately 38.91 kilograms of food. #### 38.91

Pierre wants to set up a rectangular garden in his backyard in Lyon. He has 30 meters of fencing available to enclose the garden. To maximize the area of the garden, what should be the length of the longer side of the rectangle if the shorter side is 5 meters long?

Let's solve this step by step: 1. Since Pierre wants to maximize the area of the garden, we need to express the area as a function of one variable. 2. Let's denote the length of the longer side of the rectangle as L and the shorter side as W (which we know is 5 meters). 3. The perimeter of the rectangle (the total length of the fence) is given by P = 2L + 2W. Since Pierre has 30 meters of fencing, we can write an equation: 2L + 2(5) = 30. 4. Simplifying the equation, we get: 2L + 10 = 30. 5. Subtracting 10 from both sides gives us: 2L = 20. 6. Dividing both sides by 2 yields: L = <<20 / 2 = 10>>. 7. Therefore, the length of the longer side of the rectangle should be 10 meters to maximize the area, given the shorter side is 5 meters. 8. This is because, with a fixed perimeter, a rectangle's area is maximized when it is as close to a square as possible, and with one side being 5 meters, the closest we can get to a square while still using all 30 meters of fencing is by making the other side 10 meters. #### 10

Ms. Nneoma is preparing a snack for her class. She needs to package 480 cookies into boxes that hold 12 cookies each. How many boxes can she fill with the cookies she has?

Let's break this down step by step: 1. First, we need to find out how many groups of 12 cookies Ms. Nneoma can make from 480 cookies. This is a division problem since we're sharing the cookies into equal groups. So, we divide the total number of cookies by the number of cookies each box can hold: 480 ÷ 12 = <<480/12=40>>40 2. Therefore, Ms. Nneoma can fill 40 boxes with the cookies she has. #### 40

Masha observes that the population of rabbits in a forest near Moscow doubles every 3 months. If there are currently 15 rabbits, how many will there be in 9 months?

To find out how many rabbits will be in the forest after 9 months, we need to calculate how many times the population doubles in that time frame and then apply that growth to the initial population. 1. First, we determine how many 3-month periods are in 9 months: 9 months / 3 months per doubling = <<9/3=3>>3 doublings 2. Since the population doubles every 3 months, after 3 doublings, the population increase is: 2^3 = <<2^3=8>>8 times the original population 3. Now, we apply this growth to the initial population of 15 rabbits: Final population = Initial population * Growth factor = 15 * 8 = <<15*8=120>>120 rabbits Therefore, after 9 months, there will be 120 rabbits in the forest. #### 120

Tomás has been saving money for a new bike and has $120 in his piggy bank. Every week, he adds 10% of his current savings to his piggy bank. How much money will Tomás have after 5 weeks?

Let's break this down step by step: 1. Tom\u00e1s starts with $120 in his piggy bank. 2. Each week, he adds 10% of his current savings. To find 10% of $120, we multiply by 0.10: <<120 * 0.10 = 12>> So, he adds $12 in the first week. 3. After the first week, Tom\u00e1s will have: $120 (initial savings) + $12 (added in the first week) = <<120 + 12 = 132>> 4. For the second week, he'll add 10% of $132: <<132 * 0.10 = 13.20>> Now, he has $132 + $13.20 = <<132 + 13.20 = 145.20>> 5. We repeat this process for the remaining weeks: Week 3: 10% of $145.20 = <<145.20 * 0.10 = 14.52>> Total: $145.20 + $14.52 = <<145.20 + 14.52 = 159.72>> Week 4: 10% of $159.72 = <<159.72 * 0.10 = 15.97>> Total: $159.72 + $15.97 = <<159.72 + 15.97 = 175.69>> Week 5: 10% of $175.69 = <<175.69 * 0.10 = 17.57>> Total: $175.69 + $17.57 = <<175.69 + 17.57 = 193.26>> Therefore, after 5 weeks, Tom\u00e1s will have a total of $193.26. #### 193.26

At a wildlife sanctuary in British Columbia, Canada, there are two bird aviaries. The first aviary has 15 birds and the second has 24 birds. If 7 more birds are added to the first aviary and 5 birds are released from the second aviary, how many birds are there in total now?

Let's solve this step by step: 1. First, calculate the total number of birds initially: First aviary: 15 birds Second aviary: 24 birds Total birds = 15 + 24 = <<15+24=39>>39 birds 2. Then, calculate the change in the number of birds in each aviary: First aviary: 7 birds added Second aviary: 5 birds released 3. Now, calculate the new total number of birds: First aviary: 15 + 7 = <<15+7=22>>22 birds Second aviary: 24 - 5 = <<24-5=19>>19 birds New total = 22 + 19 = <<22+19=41>>41 birds Therefore, there are 41 birds in total now. #### 41

Frau Müller is planning a school festival in Berlin and wants to make sure there is enough food for the students. She orders Bratwurst and Schnitzel in a ratio of 5:3. If she needs to serve 120 students and each student gets one item, how many Bratwurst should she order?

Let's break down the problem step by step: 1. First, we need to find the total number of parts in the ratio, which is 5 + 3 = <<5+3=8>>8. 2. Since each student gets one item, we can divide the total number of students by the total number of parts to find the multiplier for each part: 120 / 8 = <<120/8=15>>15. 3. Now, we can multiply the number of parts for Bratwurst (5) by the multiplier (15) to find the number of Bratwurst needed: 5 x 15 = <<5*15=75>>75. Therefore, Frau Müller should order 75 Bratwurst. #### 75

Fatima is making a traditional Arabic dish called kabsa for her family dinner. The recipe serves 4 people and requires 2 cups of rice. If she wants to make it for 6 people, how many cups of rice should she use?

To solve this problem, we'll use proportions since we're scaling a recipe. Let's follow the steps: 1. Understand the original recipe serves 4 people and requires 2 cups of rice. 2. Fatima wants to make the recipe for 6 people. 3. We set up a proportion to find out how many cups of rice are needed for 6 people. The proportion is (original number of people)/(new number of people) = (original amount of rice)/(new amount of rice). 4. Plugging the numbers into the proportion gives us 4/6 = 2/x, where x is the amount of rice needed for 6 people. 5. To solve for x, we cross-multiply: 4x = 6*2. 6. Then we calculate: 4x = <<6*2=12>>12. 7. Divide both sides by 4 to solve for x: x = 12/4. 8. Calculate x: x = <<12/4=3>>3. Therefore, Fatima should use 3 cups of rice for 6 people. #### 3

Kiet and his friends are planning a camping trip in Khao Yai National Park. They want to make sure they have enough snacks for the trip. If they need 3 bags of chips for every 5 people, and they have 15 people going on the trip, how many bags of chips should they buy?

Let's solve this step by step: 1. Determine the number of bags of chips needed per person: 3 bags / 5 people = <<3/5=.6>>.6 bags per person. 2. Calculate the total number of bags of chips needed for 15 people: .6 bags per person * 15 people = <<.6*15=9>>9 bags. Therefore, they should buy 9 bags of chips. #### 9

Helga is preparing Apfelstrudel for a large group of guests and needs to adjust her recipe accordingly. Her original recipe serves 8 people and requires 2 3/4 cups of flour, 1/2 cup of sugar, and 1/4 cup of butter, melted. If she wants to make 3 times the original amount, how many cups of flour will she need in total, given that for every 2 cups of flour used, she needs to add an extra 1/8 cup to ensure the dough doesn't become too dense?

To solve this, let's break down the steps needed to calculate the total amount of flour Helga will need. 1. First, we need to calculate how many cups of flour are needed for 3 times the original recipe without the extra flour for density. The original recipe requires 2 3/4 cups of flour. To make 3 times the amount, we multiply this by 3: 2 3/4 cups * 3 = <<2.75 * 3 = 8.25>>8.25 cups 2. Next, we calculate how much extra flour is needed for the density adjustment. For every 2 cups of flour, 1/8 cup is added. Since we have 8.25 cups, we divide by 2 to find out how many sets of 2 cups there are and then calculate the extra flour needed: 8.25 cups / 2 cups = <<8.25 / 2 = 4.125>>4.125 sets Since we can't have a fraction of a set for the extra flour calculation, we'll consider the whole number part (4 sets) for adding extra flour: 4 sets * 1/8 cup/set = <<4 * 0.125 = 0.5>>0.5 cups extra 3. Now, we add the extra flour to the total calculated for 3 times the recipe: 8.25 cups + 0.5 cups = <<8.25 + 0.5 = 8.75>>8.75 cups Therefore, Helga will need a total of 8.75 cups of flour to make 3 times the original amount of Apfelstrudel and ensure the dough isn't too dense. #### 8.75

Fatima wants to buy a new car as a gift for her brother on Eid al-Fitr. She deposits $5,000 into a savings account that earns a 5% annual interest rate, compounded annually. If she waits for 3 years to buy the car, how much money will she have in her account?

Let's solve this step-by-step: 1. First, we need to calculate the interest earned each year: Interest rate = 5% = 0.05 Principal amount = $5,000 Interest for the first year = Principal amount * Interest rate = $5,000 * 0.05 = <<5000 * 0.05 = 250>>$250 New balance after the first year = Principal amount + Interest = $5,000 + $250 = <<5000 + 250 = 5250>>$5,250 2. For the second and third years, we repeat the process using the new balance as the principal amount: Interest for the second year = $5,250 * 0.05 = <<5250 * 0.05 = 262.5>>$262.50 New balance after the second year = $5,250 + $262.50 = <<5250 + 262.5 = 5512.5>>$5,512.50 Interest for the third year = $5,512.50 * 0.05 = <<5512.5 * 0.05 = 275.625>>$275.63 New balance after the third year = $5,512.50 + $275.63 = <<5512.5 + 275.625 = 5788.125>>$5,788.13 Therefore, Fatima will have approximately $5,788.13 in her account after 3 years. #### 5788.13

Özge is planning a camping trip with her friends. They want to share some snacks equally among themselves. If they have 36 granola bars and there are 6 friends going on the trip, how many granola bars will each friend get if they decide to save 6 bars for a park ranger they plan to meet?

Let's solve this step by step: 1. First, calculate the total number of granola bars available for sharing among the friends after saving some for the park ranger: Total granola bars = 36, Saved for park ranger = 6 Available granola bars = Total granola bars - Saved for park ranger = <<36-6=30>>30 2. Now, divide the available granola bars by the number of friends to find out how many each friend will get: Available granola bars = 30, Number of friends = 6 Granola bars per friend = Available granola bars / Number of friends = <<30/6=5>>5 Therefore, each friend will get 5 granola bars. #### 5

Ngọc's family is planning a road trip from Hanoi to Ho Chi Minh City, a distance of 1,100 miles. Their car's fuel tank can hold 15 gallons of gasoline. If the car's fuel efficiency is 25 miles per gallon, and gasoline costs 20,000 VND per gallon, how much will they spend on fuel for the entire trip, assuming they start with a full tank and don't refill until they reach Ho Chi Minh City?

Let's solve this step-by-step: 1. First, calculate the total amount of fuel needed for the trip by dividing the total distance by the car's fuel efficiency: Total fuel needed = Total distance / Fuel efficiency Total fuel needed = 1100 miles / 25 miles/gallon Total fuel needed = <<1100 / 25 = 44>> gallons 2. Since the car's fuel tank can hold 15 gallons, and they start with a full tank, they will need to refill the tank to cover the remaining distance. 3. Calculate the remaining fuel needed after using the initial full tank: Remaining fuel needed = Total fuel needed - Fuel tank capacity Remaining fuel needed = 44 gallons - 15 gallons Remaining fuel needed = <<44 - 15 = 29>> gallons 4. Calculate the total cost of fuel by multiplying the total fuel needed by the cost per gallon: Total fuel cost = Total fuel needed * Cost per gallon Total fuel cost = 44 gallons * 20,000 VND/gallon Total fuel cost = <<44 * 20000 = 880000>> VND 5. Therefore, Ng\u1ecdc's family will spend a total of 880,000 VND on fuel for the entire trip. 6. Since the question asks for the amount they will spend, our final answer is the total fuel cost. #### 880000

Ayşe and her friends are planning a camping trip in the mountains of Turkey. They want to make sure they have enough trail mix for the hike. If they need 2/3 cup of nuts for every 3 cups of dried fruit, and they have 12 cups of dried fruit, how many cups of nuts should they bring?

Let's solve this step-by-step: 1. First, we need to determine the ratio of nuts to dried fruit. The given ratio is 2/3 cup of nuts for every 3 cups of dried fruit. 2. To find out how many cups of nuts are needed for 12 cups of dried fruit, we can set up a proportion using the given ratio: 2/3 : 3 = x : 12 3. We can then cross-multiply and solve for x: 2/3 * 12 = 3x <<2/3*12=8>> 3x = 8 x = 8 / 3 <<8/3=2.67>> 4. Therefore, Ayşe and her friends should bring 2.67 cups of nuts for the hike. #### 2.67

Mei is building a rectangular model garden with an area of 48 square feet. If the length is 3 times the width, what is the width of the garden in feet?

To find the width of the garden, let's denote the width as w and the length as l. We are given that the area of the garden is 48 square feet and that the length is 3 times the width. Step 1: Express the relationship between the length and the width as an equation. l = 3w Step 2: Use the formula for the area of a rectangle to set up an equation. Area = length * width 48 = l * w Step 3: Substitute the expression for the length (l = 3w) into the area equation. 48 = (3w) * w 48 = 3w^2 Step 4: Solve the quadratic equation for w. Divide both sides by 3 to isolate w^2: <<48 / 3 = 16>> = w^2 Take the square root of both sides to solve for w: w = sqrt(16) w = <<sqrt(16) = 4>> Step 5: Since the width cannot be negative in this context, we only consider the positive solution for w. w = 4 Therefore, the width of the garden is 4 feet. #### 4

Ariel is planning a road trip from Tel Aviv to Haifa. The distance between the two cities is 95 kilometers. If Ariel's car can travel 1/4 of the distance on a full tank of gas, and each tank of gas costs 60 shekels, how many shekels will Ariel spend on gas for the entire trip?

To find out how many shekels Ariel will spend on gas for the entire trip, we need to calculate how many tanks of gas she'll need and then multiply that by the cost of each tank. 1. First, let's find out how far Ariel's car can travel on one tank of gas. Since it can travel 1/4 of the distance on a full tank, we need to find 1/4 of the total distance: 1/4 * 95 = <<1/4 * 95 = 23.75>> kilometers 2. Now, to find out how many tanks of gas Ariel will need for the entire trip, we divide the total distance by the distance one tank can cover: 95 / 23.75 = <<95 / 23.75 = 4>> tanks 3. Since each tank costs 60 shekels, we multiply the number of tanks needed by the cost per tank to find the total cost: 4 * 60 = <<4 * 60 = 240>> shekels Therefore, Ariel will spend 240 shekels on gas for the entire trip. #### 240

Amira and her friends are planning a camping trip in the desert. They want to make a mixture of dates and nuts as a snack. The recipe calls for a ratio of 3 parts dates to 2 parts nuts. If Amira has 18 cups of dates, how many cups of nuts should she add to the mixture?

To find out how many cups of nuts Amira should add, let's follow the steps below: 1. First, we understand the ratio of dates to nuts is 3:2. This means for every 3 cups of dates, we need 2 cups of nuts. 2. We are given that Amira has 18 cups of dates. 3. To find out how many cups of nuts are needed for 18 cups of dates, we first determine how many "sets" of the ratio (3 parts dates to 2 parts nuts) fit into 18 cups of dates. Since the ratio of dates to nuts is 3:2, we divide the total amount of dates by the number representing the date's part in the ratio, which is 3. So, we divide 18 by 3 to find how many "sets" of the ratio we have: <<18 / 3 = 6>> 4. Knowing we have 6 "sets" of the ratio, we then multiply the number of sets by the part of the ratio that represents the nuts, which is 2. So, we multiply 6 sets by 2: <<6 * 2 = 12>> 5. This calculation gives us the total amount of nuts needed in cups. 6. Therefore, Amira should add 12 cups of nuts to the mixture. #### 12

Luana and her friends are organizing a camping trip in the mountains of Brazil. They want to share some snacks equally among the group. If they have 240 cookies and 3 groups of friends with different numbers of people, and the ratio of people in the groups is 2:3:5, how many cookies will each person get?

Let's break this down step by step: 1. First, we need to find the total number of parts in the ratio, which is 2 + 3 + 5 = <<2+3+5=10>>10 parts. 2. Next, we need to find the total number of people in the groups. Since the ratio of people in the groups is 2:3:5, let's assume the number of people in each group is 2x, 3x, and 5x, respectively. 3. The total number of people is 2x + 3x + 5x = 10x. 4. Since the total number of cookies is 240 and they want to share them equally among the group, we can set up a proportion: (Number of cookies) / (Total number of people) = (Number of cookies per person). 5. Substituting the values, we get 240 / 10x = Number of cookies per person. 6. To find the value of x, we need to find the total number of people. Let's assume the number of people in the first group is 2x = 2 * x = 2x people, the second group is 3x = 3 * x = 3x people, and the third group is 5x = 5 * x = 5x people. 7. Since the ratio of people is 2:3:5, the total number of people is 10x. We know that 10x people will share 240 cookies, so we can set up the equation 240 / 10x = Number of cookies per person. 8. To find the number of cookies per person, we need to find the value of x. Since the problem doesn't specify the exact number of people, we can assume x = 1 to find the number of cookies per person. Therefore, the total number of people is 10 * 1 = 10 people, and the number of cookies per person is 240 / 10 = <<240/10=24>>24 cookies per person. Therefore, each person will get 24 cookies. #### 24

Kofi is building a rectangular model of a traditional Nigerian compound. The scale model has a length of 24 inches and a width of 18 inches. If he wants to put a fence around the compound that is 3 inches away from the edges of the model, what is the area of the space between the fence and the model?

To find the area of the space between the fence and the model, we need to follow these steps: 1. Calculate the dimensions of the larger rectangle that includes the fence. Since the fence is 3 inches away from the edges of the model, we add 6 inches (3 inches on each side) to both the length and the width of the model. - New length = 24 inches + 6 inches = <<24 + 6 = 30>>30 inches - New width = 18 inches + 6 inches = <<18 + 6 = 24>>24 inches 2. Calculate the area of the larger rectangle. - Area of larger rectangle = length * width = 30 inches * 24 inches = <<30 * 24 = 720>>720 square inches 3. Calculate the area of the model itself. - Area of model = length * width = 24 inches * 18 inches = <<24 * 18 = 432>>432 square inches 4. Find the area of the space between the fence and the model by subtracting the area of the model from the area of the larger rectangle. - Area between fence and model = Area of larger rectangle - Area of model = 720 square inches - 432 square inches = <<720 - 432 = 288>>288 square inches Therefore, the area of the space between the fence and the model is 288 square inches. #### 288

Hans has been saving money for a new bike and has €120 in his savings account. His parents have agreed to give him a 5% monthly allowance to help him reach his goal of €250. However, Hans wants to buy the bike in 3 months to ride it in the upcoming German Bike Festival. If the bank offers a 2% monthly compound interest rate, will Hans have enough money to buy the bike after 3 months?

Let's solve this step-by-step: 1. First, let's calculate the monthly allowance Hans receives from his parents: 5% of \u20ac120 = <<5/100 * 120 = 6>>\u20ac6. 2. Next, we need to calculate the future value of Hans' savings using the compound interest formula: FV = PV * (1 + r)^n, where PV is the present value (\u20ac120 + \u20ac6 allowance for the first month), r is the monthly interest rate (2% = 0.02), and n is the number of periods (3 months for the interest to compound). However, since Hans receives a monthly allowance, we'll calculate the future value month by month. a) Month 1: PV = \u20ac120 + \u20ac6 = \u20ac126, FV = \u20ac126 * (1 + 0.02) = \u20ac<<126 * 1.02 = 128.52>>128.52. b) Month 2: PV = \u20ac128.52 + \u20ac6 = \u20ac134.52, FV = \u20ac134.52 * (1 + 0.02) = \u20ac<<134.52 * 1.02 = 137.22104>>137.22. c) Month 3: PV = \u20ac137.22 + \u20ac6 = \u20ac143.22, FV = \u20ac143.22 * (1 + 0.02) = \u20ac<<143.22 * 1.02 = 146.0844>>146.08. 3. Now, let's check if Hans has enough money to buy the bike after 3 months: \u20ac146.08 < \u20ac250. Hans won't have enough money to buy the bike after 3 months. #### 146.08

During a soccer game, the home team, Los Lobos, scored 2 goals in the first half. In the second half, they scored x goals, where x is represented by the quadratic equation x^2 + 5x - 6 = 0. How many goals did Los Lobos score in total?

Let's solve this step by step: 1. First, we need to solve the quadratic equation x^2 + 5x - 6 = 0 to find the number of goals scored in the second half. We can factor the quadratic equation: x^2 + 5x - 6 = (x + 6)(x - 1) = 0 This gives us two possible values for x: x + 6 = 0 or x - 1 = 0 Solving for x, we get: x = -6 or x = 1 Since the number of goals cannot be negative, we discard x = -6. Therefore, x = 1. 2. Now, we add the number of goals scored in the first half (2) to the number of goals scored in the second half (1): Total goals = 2 + 1 = <<2 + 1 = 3>> Therefore, Los Lobos scored a total of 3 goals. #### 3

Ramesh is preparing a large batch of his famous vegetable biryani for a Diwali party. The recipe calls for a ratio of 2 cups of basmati rice to 1 cup of mixed vegetables. If he wants to serve 48 people and each serving requires 1/2 cup of rice, how many cups of mixed vegetables will he need?

To solve this problem, let's break it down into steps: 1. First, we need to find out how many cups of rice Ramesh will need in total. Since each serving requires 1/2 cup of rice and he wants to serve 48 people, we multiply the number of servings by the amount of rice per serving: 48 servings * 1/2 cup/serving = <<48 * 0.5 = 24>>24 cups of rice. 2. Next, we use the given ratio of rice to vegetables, which is 2:1. This means for every 2 cups of rice, we need 1 cup of mixed vegetables. To find out how many cups of mixed vegetables are needed for 24 cups of rice, we can set up a proportion or simply divide the amount of rice by 2 since the ratio of rice to vegetables is 2:1: 24 cups of rice / 2 = <<24 / 2 = 12>>12 cups of mixed vegetables. 3. Therefore, Ramesh will need 12 cups of mixed vegetables for his vegetable biryani recipe. #### 12

Tomás is planning a backyard barbecue for his family in Rio de Janeiro. He wants to set up a rectangular picnic area with an area of 48 square meters. If the length of the picnic area is 8 meters, what is the width?

Let's solve this step by step: 1. To find the width, we need to recall the formula for the area of a rectangle, which is length times width (A = l * w). 2. We're given the area (A = 48 square meters) and the length (l = 8 meters). 3. We can rearrange the formula to solve for the width: w = A / l. 4. Plugging in the given values: w = 48 / 8. 5. Calculate the width: <<48 / 8 = 6>> Therefore, the width of the picnic area is 6 meters. #### 6

In a Nigerian high school, the student council is planning a festival. They want to make a special fruit punch that requires a ratio of 3 parts pineapple juice to 2 parts orange juice to 5 parts lemon-lime soda. If they need 2.5 liters of pineapple juice and 1.5 liters of orange juice, how many liters of lemon-lime soda should they add to maintain the desired ratio?

To solve this, let's follow the given ratio of 3 parts pineapple juice to 2 parts orange juice to 5 parts lemon-lime soda. We're given the amounts of pineapple and orange juice, and we need to find the amount of lemon-lime soda needed to maintain the ratio. 1. The given ratio of pineapple juice to orange juice to lemon-lime soda is 3:2:5. 2. We're told they need 2.5 liters of pineapple juice and 1.5 liters of orange juice. 3. To find out how many liters of lemon-lime soda are needed, we first need to determine the multiplier used to scale up from the ratio to the actual amounts of pineapple and orange juice. We can do this by dividing the actual amount of pineapple juice by its ratio part: 2.5 liters / 3 parts = <<2.5 / 3 = 0.8333>>0.8333 liters per part 4. Since the ratio of lemon-lime soda is 5 parts, we multiply the amount per part by the number of parts for lemon-lime soda: 0.8333 liters per part * 5 parts = <<0.8333 * 5 = 4.1665>>4.1665 liters 5. Therefore, the student council should add approximately 4.1665 liters of lemon-lime soda to maintain the desired ratio. #### 4.1665

Rohan's family is planning to set up a rectangular garden in their backyard in Mumbai. They want the length of the garden to be 15 meters more than the width. If they have 120 meters of fencing to enclose the garden, what should be the width of the garden so that they use up all the fencing?

To find the width of the garden, we need to use the formula for the perimeter of a rectangle, which is 2(length + width). Let's denote the width as W and the length as L. We know that L = W + 15. The perimeter is given as 120 meters, so we can set up the equation: 2(W + (W + 15)) = 120 First, simplify the equation: 2(2W + 15) = 120 Distribute the 2: 4W + 30 = 120 Subtract 30 from both sides: 4W = <<120 - 30 = 90>> Divide by 4: W = <<90 / 4 = 22.5>> Therefore, the width of the garden should be 22.5 meters. #### 22.5

Hans and his siblings, Helga and Franz, are planning a road trip from Berlin to Munich, a total distance of 550 kilometers. Their car consumes an average of 7.5 liters of gasoline per 100 kilometers. Gasoline costs 1.45 euros per liter. If they want to split the cost of gasoline equally among themselves, and they also plan to spend 50 euros each on food and accommodations, how much will each person need to contribute in total for the trip?

Let's solve this step by step: 1. First, calculate the total amount of gasoline needed for the trip: Total distance = 550 kilometers Gasoline consumption rate = 7.5 liters/100 kilometers Total gasoline needed = Total distance * (Gasoline consumption rate / 100) = 550 * (7.5 / 100) = 550 * 0.075 <<550 * 0.075 = 41.25>> liters 2. Next, calculate the total cost of gasoline: Cost of gasoline per liter = 1.45 euros Total cost of gasoline = Total gasoline needed * Cost of gasoline per liter = 41.25 * 1.45 <<41.25 * 1.45 = 59.8125>> euros 3. Since they want to split the cost of gasoline equally among themselves, and there are 3 people, we need to divide the total cost by 3: Cost per person for gasoline = Total cost of gasoline / 3 = 59.8125 / 3 <<59.8125 / 3 = 19.9375>> euros 4. Additionally, they plan to spend 50 euros each on food and accommodations. So, the total cost per person will be the sum of the cost of gasoline and the cost of food and accommodations: Total cost per person = Cost per person for gasoline + Cost of food and accommodations = 19.9375 + 50 <<19.9375 + 50 = 69.9375>> euros 5. Since we are dealing with money, we'll round the total cost per person to two decimal places: Total cost per person ≈ 69.94 euros Therefore, each person will need to contribute approximately 69.94 euros for the trip. #### 69.94

Minh observes that for every 5 birds in the forest, there are 3 squirrels. If he counts 15 birds, how many squirrels should he expect to see?

Let's solve this step by step: 1. First, we need to establish the ratio of birds to squirrels as given: 5 birds to 3 squirrels. 2. Since Minh counts 15 birds, we need to find how many groups of 5 birds are there in 15 birds: 15 / 5 = <<15/5=3>>3. 3. Since for every 5 birds there are 3 squirrels, we multiply the number of groups of birds by the number of squirrels per group: 3 * 3 = <<3*3=9>>9. Therefore, Minh should expect to see 9 squirrels. #### 9

Kofi saves 15,000 Ghanaian cedis on January 1st to buy a new sound system for the upcoming Akwasidae festival. His savings account earns a 6% annual interest compounded monthly. If he doesn't make any withdrawals, how much money will Kofi have in his account by December 31st of the same year?

To solve this problem, we need to calculate the compound interest earned on Kofi's savings account. 1. First, we need to convert the annual interest rate to a monthly rate since the interest is compounded monthly. The annual rate is 6%, so the monthly rate is: 6%/year / 12 months/year = 0.5%/month = <<6/12=0.5>>0.5%/month 2. Convert the monthly rate to a decimal for calculation purposes: 0.5% = 0.005 in decimal form = <<0.5/100=0.005>>0.005 3. The initial principal amount is 15,000 Ghanaian cedis. We will use the formula for compound interest, A = P(1 + r)^n, where A is the amount after interest, P is the principal amount, r is the monthly interest rate, and n is the number of periods. Since the interest is compounded monthly for a year, n = 12 months: A = 15000(1 + 0.005)^12 4. Calculate the amount after 12 months, including interest: A = 15000(1.005)^12 = 15000 * 1.061678 = <<15000*1.061678=15925.17>>15925.17 5. Therefore, Kofi will have 15,925.17 Ghanaian cedis in his account by December 31st of the same year. #### 15925.17

Ngọc is planning a road trip from Hanoi to Ho Chi Minh City, a distance of 1,100 miles. If she drives 220 miles on the first day and 280 miles on the second day, how many miles does she still have to travel to reach her destination?

Let's solve this step by step: 1. Ng\u1ecdc starts with a total distance of 1,100 miles to travel. 2. On the first day, she drives 220 miles, so we subtract that from the total distance: <<1100 - 220 = 880>> 3. On the second day, she drives another 280 miles, so we subtract that from the remaining distance: <<880 - 280 = 600>> Therefore, Ng\u1ecdc still has 600 miles to travel to reach her destination. #### 600

Luis has 15 birds in his aviary in Rio de Janeiro, and he wants to build a rectangular enclosure with an area that can accommodate all the birds. If the length of the enclosure is 5 meters, what should be the width to ensure each bird has 0.5 square meters of space?

Let's break down the problem step by step: 1. First, calculate the total area required for all the birds: Each bird needs 0.5 square meters, and there are 15 birds. Total area = number of birds * area per bird = 15 * 0.5 = <<15*0.5=7.5>>7.5 square meters 2. The area of the rectangular enclosure is given by length * width. We are given the length as 5 meters, and we want to find the width. Area = length * width 7.5 = 5 * width 3. To find the width, divide both sides by 5: width = 7.5 / 5 = <<7.5/5=1.5>>1.5 meters Therefore, the width of the enclosure should be 1.5 meters to ensure each bird has 0.5 square meters of space. #### 1.5

Yael, a wildlife observer in Israel, notes that the population of a certain bird species in the Hula Valley has increased by 25% each year for the past three years. If the initial population was 120 birds, how many birds are there now?

To find the current population of the bird species, we'll calculate the increase over the three years step by step. 1. First, we find the population after the first year's increase: The initial population is 120 birds. The increase is 25% of 120, which is 0.25 * 120 = <<0.25*120=30>>30 birds. So, after the first year, the population is 120 + 30 = <<120+30=150>>150 birds. 2. Next, we calculate the population after the second year's increase: The population after the first year is 150 birds. The increase is 25% of 150, which is 0.25 * 150 = <<0.25*150=37.5>>37.5 birds. So, after the second year, the population is 150 + 37.5 = <<150+37.5=187.5>>187.5 birds. 3. Finally, we calculate the population after the third year's increase: The population after the second year is 187.5 birds. The increase is 25% of 187.5, which is 0.25 * 187.5 = <<0.25*187.5=46.875>>46.875 birds. So, after the third year, the population is 187.5 + 46.875 = <<187.5+46.875=234.375>>234.375 birds. Therefore, after three years, there are 234.375 birds, but since we can't have a fraction of a bird, we'll round to the nearest whole number for practical purposes. However, the question does not explicitly ask for rounding, so we'll provide the precise calculation result. #### 234.375

Nguyễn Thị Mai has a budget of ₫5,000,000 to buy school supplies. She needs to buy at least 3 textbooks that cost ₫200,000 each, 5 notebooks that cost ₫50,000 each, and pens that cost ₫20,000 per pack. How many packs of pens can she buy to maximize her remaining budget after purchasing the required textbooks and notebooks?

Let's solve this step-by-step: 1. Calculate the total cost of the textbooks: 3 textbooks * \u20ab200,000 per textbook = <<3 * 200000 = 600000>>\u20ab600,000 2. Calculate the total cost of the notebooks: 5 notebooks * \u20ab50,000 per notebook = <<5 * 50000 = 250000>>\u20ab250,000 3. Calculate the remaining budget after purchasing the textbooks and notebooks: \u20ab5,000,000 - \u20ab600,000 - \u20ab250,000 = <<5000000 - 600000 - 250000 = 4150000>>\u20ab4,150,000 4. Calculate how many packs of pens Nguy\u1ec5n Th\u1ecb Mai can buy with the remaining budget: \u20ab4,150,000 / \u20ab20,000 per pack = <<4150000 / 20000 = 207.5>>207.5 packs Since she can't buy a fraction of a pack, we round down to 207 packs to stay within budget. Therefore, Nguy\u1ec5n Th\u1ecb Mai can buy 207 packs of pens to maximize her remaining budget. #### 207

Tom's Taco Truck is catering for a large event and needs to triple their recipe for vegetarian chili. If the original recipe calls for 2 cups of diced tomatoes and 1 cup of kidney beans, and a can of diced tomatoes is 1.5 cups and a can of kidney beans is 0.75 cups, how many cans of each should Tom buy to have enough for the tripled recipe?

To solve this problem, let's break it down into steps. 1. First, we need to calculate the total amount of diced tomatoes and kidney beans needed for the tripled recipe. For diced tomatoes: 2 cups * 3 = <<2*3=6>>6 cups. For kidney beans: 1 cup * 3 = <<1*3=3>>3 cups. 2. Next, we determine how many cans of each Tom needs to buy. For diced tomatoes: 6 cups / 1.5 cups per can = <<6/1.5=4>>4 cans. For kidney beans: 3 cups / 0.75 cups per can = <<3/0.75=4>>4 cans. Therefore, Tom should buy 4 cans of diced tomatoes and 4 cans of kidney beans. #### 4

Tomás is planning a camping trip in the mountains of Chihuahua and wants to set up a rectangular tent that is 12 meters long and 8 meters wide. If the tent has a height of 4 meters, what is the volume of the tent in cubic meters?

To find the volume of the tent, we can use the formula for the volume of a rectangular prism, which is length times width times height. 1. First, we identify the dimensions of the tent: length = 12 meters, width = 8 meters, and height = 4 meters. 2. Next, we apply the formula for volume: Volume = length * width * height. 3. Plug in the values: Volume = 12 * 8 * 4. 4. Multiply the length and width: 12 * 8 = <<12*8=96>>96. 5. Then multiply the result by the height: 96 * 4 = <<96*4=384>>384. Therefore, the volume of the tent is 384 cubic meters. #### 384

The Wildlife Conservation Society of India is tracking the population of Bengal tigers in the Sundarbans National Park. The data shows that the tiger population has been increasing at an average rate of 5% per year. If there were 250 tigers in 2018 and 300 tigers in 2022, what is the expected population of Bengal tigers in 2025, assuming the growth rate remains constant?

To find the expected population of Bengal tigers in 2025, we first need to determine the exact growth rate per year based on the information given. The population increased from 250 in 2018 to 300 in 2022, which is over 4 years. 1. Calculate the total growth over 4 years: The initial population was 250, and the final population was 300. The increase is 300 - 250 = <<300-250=50>>50 tigers over 4 years. 2. Calculate the annual growth rate: We already know the growth rate is 5% per year, but let's confirm it matches the data given. The formula for compound annual growth rate (CAGR) is: \( \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{\text{Number of Periods}}} - 1 \) However, since we're given the growth rate, we will directly apply it. 3. Apply the growth rate to find the population in 2025: From 2022 to 2025 is 3 years. We apply the 5% growth rate for each of these years. The formula for future value \( FV \) after \( n \) years with a growth rate \( r \) is: \( FV = PV \times (1 + r)^n \), where \( PV \) is the present value (population in 2022), \( r \) is the annual growth rate (5% or 0.05 as a decimal), and \( n \) is the number of years (3 years from 2022 to 2025). So, for 2025: \( FV_{2025} = 300 \times (1 + 0.05)^3 \) \( FV_{2025} = 300 \times (1.05)^3 \) \( FV_{2025} = 300 \times 1.157625 \) \( FV_{2025} = <<300*1.157625=347.2875>>347.2875 \) Since we cannot have a fraction of a tiger, we round to the nearest whole number: \( FV_{2025} \approx 347 \) Therefore, the expected population of Bengal tigers in 2025 is approximately 347. #### 347

Anaïs, a traveler from Mexico City, invested 5,000 pesos in a savings account with a 6% annual interest rate compounded annually. If she plans to use this money for a trip to Japan in 2 years, how much will she have in her account by then?

To solve this problem, we'll break it down into steps. 1. First, we need to calculate the amount of money Anaís will have after the first year of compound interest: The formula for compound interest is A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (in decimal), and n is the number of years. Given P = 5,000 pesos, r = 6% or 0.06 as a decimal, and n = 1 year for the first year: A = 5000(1 + 0.06)^1 = 5000 * 1.06 = <<5000 * 1.06 = 5300>>5,300 pesos after the first year. 2. Now, we calculate the amount after the second year, using the result from the first year as the new principal: A = 5300(1 + 0.06)^1 = 5300 * 1.06 = <<5300 * 1.06 = 5618>>5,618 pesos after the second year. Therefore, Anaís will have 5,618 pesos in her account after 2 years. #### 5618

François is planning a trip to visit his grandparents in Lyon, France. He invests €1,000 in a savings account that earns a 5% annual interest rate, compounded annually. If he invests the money for 3 years, how much will he have to spend on his trip?

To find the total amount after 3 years, we'll use the compound interest formula: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (in decimal), and n is the number of years. 1. Convert the interest rate to decimal: 5% = <<5 / 100 = 0.05>>0.05 2. Plug in the values into the formula: A = 1000(1 + 0.05)^3 3. Calculate the amount after 3 years: A = 1000 * (1.05)^3 = 1000 * <<1.05 ^ 3 = 1.157625>>1.157625 = <<1000 * 1.157625 = 1157.625>>1157.625 Therefore, François will have approximately €1157.63 to spend on his trip. #### 1157.63

Sergei is planning a road trip from Moscow to St. Petersburg, which is 715 kilometers away. If his car's fuel tank can hold 50 liters of gasoline and the car consumes 10 liters per 100 kilometers, how many times will Sergei need to refuel his car during the trip, assuming he starts with a full tank and there are fuel stations along the way where he can refuel?

To solve this problem, we need to calculate how far Sergei can travel on a full tank and then determine how many times he needs to refuel to cover the total distance. 1. Calculate the distance Sergei can travel on a full tank: Distance per liter = 100 km / 10 liters = <<100/10=10>>10 km/liter Total distance per full tank = 10 km/liter * 50 liters = <<10*50=500>>500 km 2. Calculate how many times Sergei needs to refuel: Total distance = 715 km Distance covered by the initial full tank = 500 km Remaining distance = 715 km - 500 km = <<715-500=215>>215 km Since Sergei can travel 500 km on a full tank, for the remaining 215 km, he will need a fraction of a tank: Fraction of the tank needed for the remaining distance = 215 km / 500 km = <<215/500=0.43>>0.43 Since Sergei cannot refuel a fraction of a tank, we round up to the nearest whole number to ensure he has enough fuel for the entire trip. However, in this context, rounding is not explicitly needed because the question implicitly asks for how many times he will need to refuel, not how many full tanks he will need. Sergei starts with a full tank, so for the remaining distance that is less than what a full tank can cover, he only needs to refuel once to top off for the remaining distance, not a full tank. Therefore, Sergei will need to refuel once to cover the remaining distance after the initial full tank. #### 1

Luisa is making tamales for the Day of the Dead celebration and wants to package them in the most cost-effective way. She has two types of containers: small ones that hold 6 tamales and cost $0.50 each, and large ones that hold 12 tamales and cost $0.90 each. Luisa needs to package 60 tamales. How many of each type of container should she buy to minimize her total cost?

To minimize the total cost, Luisa needs to find the combination of small and large containers that will hold exactly 60 tamales at the lowest cost. Let's denote the number of small containers as x and the number of large containers as y. 1. First, we need to set up the equation based on the number of tamales each container can hold: 6x + 12y = 60 2. To make it simpler, we can divide the entire equation by 6: x + 2y = 10 3. Since Luisa wants to minimize her cost, she should use as many large containers as possible because they are more cost-effective per tamale. However, she should also use some small containers if necessary, to exactly reach 60 tamales without exceeding it. 4. The cost equation is 0.50x + 0.90y. To minimize cost, we want to minimize x and maximize y without violating the constraint from step 2. 5. From step 2, to maximize y without exceeding the limit, we find y by dividing 10 by 2 (since 2y is in the equation): y = <<10 / 2 = 5>> 6. Now, substitute y back into the simplified equation to find x: x + 2(5) = 10 x + 10 = 10 x = <<10 - 10 = 0>> 7. Calculate the total cost using the values of x and y: Total Cost = 0.50x + 0.90y Total Cost = 0.50 * 0 + 0.90 * 5 Total Cost = 0 + 4.50 Total Cost = <<0 + 4.50 = 4.50>> Therefore, Luisa should buy 0 small containers and 5 large containers to minimize her total cost to $4.50. #### 4.50

Maya is shopping at the Carmel Market in Tel Aviv and wants to buy 3/4 kilogram of dates. If the vendor only sells dates in 1/8 kilogram packages, how many packages should Maya buy to have exactly 3/4 kilogram of dates?

To find out how many packages Maya needs to buy, let's break this down step by step: 1. First, we need to convert the fraction of the amount Maya wants to buy into a form that matches the package size. The least common multiple of 8 and 4 is 8. So, we convert 3/4 into eighths: 3/4 = 6/8 because 4*2 = 8 and 3*2 = 6 Now, we know Maya wants 6/8 kilograms of dates. 2. Since the vendor sells dates in 1/8 kilogram packages, we can directly compare the fractions: Maya needs 6/8 kilograms, so she needs 6 packages of 1/8 kilogram each. Therefore, Maya should buy <<6=6>>6 packages of dates to have exactly 3/4 kilogram. #### 6

The Adebayo family is planning a road trip from Lagos to Abuja, a distance of 450 miles. The probability of encountering a traffic jam in the first 150 miles is 0.4. If they encounter a traffic jam, they will take a detour that adds 30 miles to their trip. What is the expected total distance the Adebayo family will travel?

To find the expected total distance the Adebayo family will travel, we need to consider both scenarios: encountering a traffic jam and not encountering a traffic jam. 1. Calculate the distance if they encounter a traffic jam: - Initial distance: 450 miles - Additional distance due to detour: 30 miles - Total distance with traffic jam = 450 + 30 = <<450 + 30 = 480>> miles 2. Calculate the distance if they do not encounter a traffic jam: - The distance remains the original 450 miles. 3. Calculate the expected total distance using the probabilities: - Probability of encountering a traffic jam: 0.4 - Probability of not encountering a traffic jam: 1 - 0.4 = <<1 - 0.4 = 0.6>> - Expected total distance = (Probability of traffic jam * Distance with traffic jam) + (Probability of no traffic jam * Distance without traffic jam) - Expected total distance = (0.4 * 480) + (0.6 * 450) - Expected total distance = <<0.4 * 480 = 192>> + <<0.6 * 450 = 270>> - Expected total distance = 192 + 270 = <<192 + 270 = 462>> miles Therefore, the expected total distance the Adebayo family will travel is 462 miles. #### 462

Tom has been saving money for a new bike and has $120 in his savings account. Each week, he earns $15 by walking his neighbor's dog. If he spends $8 per week on snacks, how many weeks will it take him to have enough money to buy a bike that costs $180?

Let's solve this step by step: 1. First, calculate how much more money Tom needs to buy the bike: Money needed = Price of bike - Money already saved Money needed = $180 - $120 <<180 - 120 = 60>> Money needed = $60 2. Next, calculate how much Tom saves each week after spending money on snacks: Weekly savings = Money earned - Money spent on snacks Weekly savings = $15 - $8 <<15 - 8 = 7>> Weekly savings = $7 3. Now, calculate how many weeks it will take Tom to save enough money to buy the bike: Number of weeks = Money needed / Weekly savings Number of weeks = $60 / $7 <<60 / 7 = 8.57>> Since we cannot have a fraction of a week, we round up to the nearest whole number because Tom cannot buy the bike until he has enough money. Number of weeks = 9 Therefore, it will take Tom 9 weeks to have enough money to buy the bike. #### 9

Akua is planning a road trip from Lagos to Abuja, a distance of 450 miles. Her car's fuel tank can hold 15 gallons, and the fuel efficiency is 30 miles per gallon. If fuel costs 250 Nigerian naira per gallon, and she already has 2,000 naira for the trip, how much more money will she need to buy enough fuel for the entire trip?

Let's solve this step by step: 1. First, calculate the total amount of fuel needed for the trip by dividing the total distance by the fuel efficiency: Total fuel = Total distance / Fuel efficiency = 450 miles / 30 miles/gallon = <<450 / 30 = 15>>15 gallons 2. Since Akua's car can hold exactly 15 gallons, she will need to fill up the tank completely for the trip. 3. Calculate the total cost of the fuel by multiplying the amount of fuel needed by the cost per gallon: Total fuel cost = Total fuel * Cost per gallon = 15 gallons * 250 naira/gallon = <<15 * 250 = 3750>>3750 naira 4. Akua already has 2000 naira, so we need to find out how much more money she needs to buy enough fuel for the entire trip: Additional money needed = Total fuel cost - Money Akua already has = 3750 naira - 2000 naira = <<3750 - 2000 = 1750>>1750 naira Therefore, Akua will need 1750 naira more to buy enough fuel for the entire trip. #### 1750

Mei-Ling invests $500 in a savings account that earns a 5% annual interest rate compounded annually. If she opens the account on Chinese New Year and doesn't make any withdrawals, how much money will she have after 5 years?

To find out how much money Mei-Ling will have after 5 years, we need to calculate the compound interest earned on her investment. Here's the step-by-step solution: 1. First, we need to calculate the interest rate fraction: 5% = 5/100 = <<5/100=0.05>>0.05. 2. Next, we'll use the formula for compound interest: A = P(1 + r)^n, where A is the amount after n years, P is the principal amount ($500 in this case), r is the annual interest rate (0.05), and n is the number of years (5). 3. Now, let's substitute the values into the formula: A = 500(1 + 0.05)^5. 4. Calculate the value inside the parentheses first: (1 + 0.05) = <<1+0.05=1.05>>1.05. 5. Raise 1.05 to the power of 5: 1.05^5 = <<1.05^5=1.2762815625>>1.2762815625. 6. Multiply the principal amount by the result: 500 * 1.2762815625 = <<500*1.2762815625=638.14078125>>638.14078125. Therefore, Mei-Ling will have $638.14 after 5 years. #### 638.14

Leticia is planning a trip from Rio de Janeiro to São Paulo, a distance of 450 kilometers. If her car's fuel efficiency is 12 kilometers per liter and gas costs R$ 5.50 per liter, what is the total fuel cost for the trip if she also has to pay a 10% tax on the fuel?

To find the total fuel cost for Leticia's trip, we'll break down the problem into steps. 1. Calculate how many liters of fuel the trip will consume: Total distance = 450 kilometers Fuel efficiency = 12 kilometers per liter Fuel consumption = Total distance / Fuel efficiency = <<450 / 12 = 37.5>> liters 2. Calculate the cost of the fuel without tax: Fuel cost without tax = Fuel consumption * Cost per liter = <<37.5 * 5.50 = 206.25>> R$ 3. Calculate the 10% tax on the fuel cost: Tax amount = 10% of Fuel cost without tax = <<206.25 * 10 / 100 = 20.625>> R$ 4. Calculate the total fuel cost including tax: Total fuel cost = Fuel cost without tax + Tax amount = <<206.25 + 20.625 = 226.875>> R$ 5. Round the total fuel cost to two decimal places for currency: Total fuel cost = <<226.875 = 226.88>> R$ Therefore, the total fuel cost for Leticia's trip is R$226.88. #### 226.88

During the Day of the Dead celebration, Ana's family makes 36 traditional sugar skulls to give to their friends and relatives. They decide to randomly decorate 3/4 of them with bright colors and the rest with pastel colors. If Ana's brother randomly selects one of the sugar skulls, what is the probability that it will be decorated with bright colors?

To find the probability that Ana's brother selects a sugar skull decorated with bright colors, we need to first determine how many sugar skulls are decorated with bright colors and then calculate the probability of selecting one of those. 1. Calculate the number of sugar skulls decorated with bright colors: Total sugar skulls = 36 Fraction decorated with bright colors = 3/4 Number of sugar skulls with bright colors = Total sugar skulls * Fraction decorated with bright colors = 36 * 3/4 = <<36*3/4=27>>27 2. Calculate the probability of selecting a sugar skull decorated with bright colors: Probability = Number of sugar skulls with bright colors / Total sugar skulls = 27 / 36 = <<27/36=0.75>>0.75 Therefore, the probability that Ana's brother selects a sugar skull decorated with bright colors is 0.75. #### 0.75

At the annual Fiesta de la Vida in Santa Fe, a game stall offers a challenge involving three jars filled with different colored marbles. Jar A contains 15 red marbles and 5 blue marbles, Jar B contains 12 green marbles and 8 yellow marbles, and Jar C contains 20 purple marbles and 10 orange marbles. To win, a player must randomly select one marble from each jar in sequence, starting with Jar A, then Jar B, and finally Jar C, without replacement. What is the probability that a player will select a blue marble from Jar A, followed by a yellow marble from Jar B, and finally an orange marble from Jar C?

To find the probability of selecting a blue marble from Jar A, followed by a yellow marble from Jar B, and finally an orange marble from Jar C, we need to calculate the probability of each event and then multiply them together since these are dependent events. 1. Probability of selecting a blue marble from Jar A: - Total marbles in Jar A = 15 red + 5 blue = <<15+5=20>>20 marbles - Probability of selecting a blue marble from Jar A = Number of blue marbles / Total marbles in Jar A = 5 / 20 = 1 / 4 = <<5/20=0.25>>0.25 2. Probability of selecting a yellow marble from Jar B after selecting a blue marble from Jar A: - Total marbles in Jar B = 12 green + 8 yellow = <<12+8=20>>20 marbles - Probability of selecting a yellow marble from Jar B = Number of yellow marbles / Total marbles in Jar B = 8 / 20 = 2 / 5 = <<8/20=0.4>>0.4 3. Probability of selecting an orange marble from Jar C after selecting a yellow marble from Jar B: - Total marbles in Jar C = 20 purple + 10 orange = <<20+10=30>>30 marbles - Probability of selecting an orange marble from Jar C = Number of orange marbles / Total marbles in Jar C = 10 / 30 = 1 / 3 = <<10/30=0.3333333333333333>>0.3333333333333333 Now, we multiply the probabilities of each step to find the overall probability of the sequence of events: Overall probability = Probability of blue from A * Probability of yellow from B * Probability of orange from C = 0.25 * 0.4 * 0.3333333333333333 = <<0.25*0.4*0.3333333333333333=0.03333333333333333>>0.03333333333333333 Rounded to four decimal places, the probability is approximately 0.0333. #### 0.0333

The Patel family is planning a road trip from Toronto to Vancouver. They have two vehicles: a car that can travel 400 km on a full tank and a van that can travel 500 km. Gas costs $1.20 per liter, and the car's tank holds 60 liters, while the van's tank holds 80 liters. If they want to drive a total of 4,300 km and the car will drive 1,800 km of that, how much will they spend on gas for the car?

To find out how much the Patel family will spend on gas for the car, we need to calculate how many liters of gas the car will use and then multiply that by the cost per liter. 1. First, determine how many full tanks the car will need for 1,800 km: Since the car can travel 400 km on a full tank, divide the total distance by the distance per tank: 1,800 km / 400 km/tank = <<1800/400=4.5>>4.5 tanks 2. Since the car cannot use a fraction of a tank, this means it will need 5 full tanks to cover the distance without running out of gas during the trip. 3. Calculate the total liters of gas the car will use: The car's tank holds 60 liters, and it will need 5 tanks: 60 liters/tank * 5 tanks = <<60*5=300>>300 liters 4. Calculate the total cost of gas for the car: Multiply the total liters by the cost per liter: 300 liters * $1.20/liter = $<<300*1.2=360>>360 Therefore, the Patel family will spend $360 on gas for the car. #### 360

Taro Yamada, a Japanese high school baseball coach, noticed that the number of home runs his team hits each season has been decreasing by 15% every year. If the team hit 25 home runs in the previous season, how many home runs can Coach Yamada expect his team to hit in 3 years?

Let's solve this step by step: 1. The number of home runs decreases by 15% each year. To find the decrease multiplier, we subtract 15% from 100%: 100% - 15% = <<100 - 15 = 85>>85% or 0.85. 2. Starting with 25 home runs, we apply the decrease for the first year: 25 * 0.85 = <<25 * 0.85 = 21.25>>21.25 home runs. 3. For the second year, we apply the decrease again: 21.25 * 0.85 = <<21.25 * 0.85 = 18.0625>>18.0625 home runs. 4. For the third year, we apply the decrease one more time: 18.0625 * 0.85 = <<18.0625 * 0.85 = 15.353125>>15.353125 home runs. 5. Since we cannot have a fraction of a home run, we round to the nearest whole number. However, the task asks for the exact calculation result before rounding. Therefore, Coach Yamada can expect his team to hit approximately 15.353125 home runs in 3 years, but for precision in our format, we do not round. #### 15.353125

Amara is planning a road trip from Lagos to Abuja, a distance of 450 miles. Her car has a fuel tank that can hold 15 gallons of gas, and the fuel efficiency is 30 miles per gallon. If gas costs $2.50 per gallon, and she already has $20 worth of gas in her tank, how much more money will she need to buy enough gas for the entire trip?

Let's break this down step by step: 1. First, we need to calculate how many miles Amara can travel with the gas she already has. Since gas costs $2.50 per gallon, and she has $20 worth of gas, we can calculate the amount of gas she has in gallons: $20 / $2.50 per gallon = <<20 / 2.5 = 8>> gallons 2. Now, we can calculate the distance she can travel with this amount of gas, given the fuel efficiency of 30 miles per gallon: 8 gallons * 30 miles per gallon = <<8 * 30 = 240>> miles 3. Since the total distance of the trip is 450 miles, we can calculate how many more miles she needs to cover: 450 miles - 240 miles = <<450 - 240 = 210>> miles 4. Next, we can calculate how many gallons of gas she needs to buy to cover this remaining distance: 210 miles / 30 miles per gallon = <<210 / 30 = 7>> gallons 5. Finally, we can calculate the cost of the additional gas she needs to buy: 7 gallons * $2.50 per gallon = <<7 * 2.5 = 17.5>> dollars Therefore, Amara needs $17.50 more to buy enough gas for the entire trip. #### 17.5

La famille Dupont prévoit une réunion de famille et souhaite louer un grand chapiteau pour abriter tous les invités. Le coût de location du chapiteau est de 200$ plus 5$ par personne au-delà de 50 personnes. Si x représente le nombre de personnes au-delà de 50, établissez une équation quadratique pour représenter le coût total de location du chapiteau, étant donné que le coût total est de 800$. Quelle est la valeur de x ?

Pour résoudre ce problème, nous allons établir une équation quadratique pour représenter le coût total de location du chapiteau. 1. Le coût de location du chapiteau est de 200$ plus 5$ par personne au-delà de 50 personnes. Si x représente le nombre de personnes au-delà de 50, alors le coût total peut être représenté par l'équation : Coût total = 200 + 5x 2. On sait que le coût total est de 800$. On peut donc établir l'équation : 200 + 5x = 800 3. Maintenant, nous allons résoudre l'équation pour trouver la valeur de x. Tout d'abord, nous allons soustraire 200 des deux côtés de l'équation : 5x = 800 - 200 5x = <<800 - 200 = 600>> 4. Ensuite, nous allons diviser les deux côtés de l'équation par 5 pour trouver la valeur de x : x = 600 / 5 x = <<600 / 5 = 120>> Par conséquent, la valeur de x est 120. #### 120

Ngọc and her family are planning a road trip from Hanoi to Ho Chi Minh City, a distance of 1,700 kilometers. If they drive 5 hours a day, and their car's fuel consumption is 10 kilometers per liter, how many liters of fuel will they need for the entire trip, assuming they maintain a constant speed?

Let's break down the problem step by step: 1. First, we need to find the total number of hours they will drive for the entire trip. Since they drive 5 hours a day, we divide the total distance by the speed to find the total hours, but the speed is not given. However, we can proceed with the daily distance covered. 2. Daily distance covered = speed * time. Since speed is not directly given, we'll calculate it from the fuel consumption and given distance. 3. The car's fuel consumption is 10 kilometers per liter. To find out how many kilometers they cover in a day, we first need the daily fuel consumption, which isn't directly calculable without the speed. However, we can rearrange the information given to solve for total fuel needed directly by dividing the total distance by the fuel efficiency. 4. Total fuel needed = Total distance / Fuel efficiency 5. Total fuel needed = 1700 km / 10 km/liter = <<1700/10=170>>170 liters Therefore, Ng\u1ecdc and her family will need 170 liters of fuel for the entire trip. #### 170

Tomás is the coach of a local soccer team in Mexico City. His team won 3/4 of their games last season. If they played a total of 24 games, how many games did they win?

To find out how many games Tomás' team won, we need to calculate 3/4 of the total games played. 1. First, let's identify the total number of games, which is given as 24. 2. Now, we calculate 3/4 of 24 to find the number of games won: 3/4 * 24 = <<3/4*24=18>> Therefore, Tomás' team won 18 games. #### 18

Pierre travels from Paris to Lyon, a distance of 470 km. If he drives for 3/4 of the distance at an average speed of 120 km/h, and then takes a break before driving the remaining distance at 90 km/h, how many hours in total does he spend driving?

Let's solve this step by step: 1. First, calculate the distance Pierre drives at 120 km/h, which is 3/4 of the total distance: 3/4 * 470 km = <<3/4 * 470 = 352.5>> km 2. Calculate the time Pierre spends driving this distance at 120 km/h: Time = Distance / Speed = 352.5 km / 120 km/h = <<352.5 / 120 = 2.9375>> hours 3. Next, calculate the remaining distance, which is 1/4 of the total distance: 1/4 * 470 km = <<1/4 * 470 = 117.5>> km 4. Calculate the time Pierre spends driving this distance at 90 km/h: Time = Distance / Speed = 117.5 km / 90 km/h = <<117.5 / 90 = 1.3056>> hours 5. Finally, add the times spent driving at both speeds to get the total time: Total Time = 2.9375 hours + 1.3056 hours = <<2.9375 + 1.3056 = 4.2431>> hours Therefore, Pierre spends approximately 4.24 hours driving. #### 4.24

Tom is building a scale model of a World War II aircraft with a wingspan of 120 feet. If the scale of the model is 1:48, how many inches long should the wingspan of the model be?

To find the wingspan of the model, we first need to convert the actual wingspan from feet to inches because the scale is usually applied to the same units. There are 12 inches in a foot. 1. Convert 120 feet to inches: 120 feet * 12 inches/foot = <<120*12=1440>>1440 inches 2. Now, apply the scale of 1:48 to find the model's wingspan in inches. The scale factor is 1/48. 3. Multiply the actual wingspan in inches by the scale factor: 1440 inches * (1/48) = <<1440*(1/48)=30>>30 inches Therefore, the wingspan of the model should be 30 inches. #### 30

Ayşe invests 500 Turkish Lira in a savings account that earns a 6% annual interest rate, compounded annually. After two years, she withdraws the interest earned and uses it to buy camping gear for a trip to Ölüdeniz Beach. If she then invests the remaining amount for another year at the same interest rate, what will be the total amount in her account?

To solve this, let's break it down into steps: 1. First, calculate the amount in the account after two years of compound interest: The formula for compound interest is A = P(1 + r)^n, where A is the amount after n years, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), and n is the number of years. Given P = 500 Turkish Lira, r = 6% or 0.06 as a decimal, and n = 2 years, we can calculate A: A = 500(1 + 0.06)^2 = 500 * (1.06)^2 = 500 * <<1.06^2=1.1236>>1.1236 = <<500*1.1236=561.8>>561.8 Turkish Lira So, after two years, Ayşe has 561.8 Turkish Lira in her account. 2. Next, we need to find out how much interest was earned over these two years: Interest = Amount after 2 years - Initial Investment = 561.8 - 500 = <<561.8-500=61.8>>61.8 Turkish Lira This interest is withdrawn, leaving Ayşe with her initial investment of 500 Turkish Lira in the account. 3. Now, calculate the amount in the account after investing the remaining 500 Turkish Lira for another year at the same 6% interest rate: Using the compound interest formula again with P = 500, r = 0.06, and n = 1: A = 500(1 + 0.06)^1 = 500 * 1.06 = <<500*1.06=530>>530 Turkish Lira Therefore, the total amount in Ayşe's account after the third year will be 530 Turkish Lira. #### 530

Ana's Abuela is famous for her flan recipe that serves 8 people. If Ana wants to make 25% more flan for a family gathering, and the original recipe calls for 3 cups of sugar, how many cups of sugar will Ana need for the larger batch?

Let's solve this step by step: 1. First, we need to find out how many people Ana wants to serve with the larger batch. Since she wants to make 25% more flan, we calculate 25% of the original number of people served: 25% of 8 = <<25/100*8=2>>2 more people 2. Add this to the original number of people to find the new total: 8 + 2 = <<8+2=10>>10 people 3. Since the recipe scales linearly with the number of people, we need to find the scaling factor for the ingredients. This is the ratio of the new number of people to the original number: 10 / 8 = <<10/8=1.25>>1.25 4. Now, we apply this scaling factor to the original amount of sugar: 3 cups * 1.25 = <<3*1.25=3.75>>3.75 cups Therefore, Ana will need 3.75 cups of sugar for the larger batch. #### 3.75

Fatima is planning a trip from Dubai to Cairo. The flight from Dubai to Cairo takes 2 hours and 30 minutes, and the time difference between the two cities is 1 hour. If Fatima's flight departs from Dubai at 10:00 AM local time, what will be the local time in Cairo when she arrives?

Let's solve this step by step: 1. First, we need to calculate the arrival time in Dubai time. Since the flight takes 2 hours and 30 minutes, we add this to the departure time of 10:00 AM. 10:00 AM + 2 hours = 12:00 PM 12:00 PM + 30 minutes = 12:30 PM 2. Now, we need to adjust for the time difference between Dubai and Cairo. Cairo is 1 hour behind Dubai. 12:30 PM - 1 hour = 11:30 AM Therefore, when Fatima arrives in Cairo, the local time will be 11:30 AM. Since we are asked for the time, and assuming we need to convert this into a 24-hour format for a numeric answer, the time in 24-hour format is: 11:30 AM = 11.5 hours past midnight #### 11.5