# Percents

## Solve General Applications of Percent


### Translate and Solve Basic Percent Equations

We will solve percent equations by using the methods we used to solve equations with fractions or decimals. In the past, you may have solved percent problems by setting them up as proportions. That was the best method available when you did not have the tools of algebra. Now as a prealgebra student, you can translate word sentences into algebraic equations, and then solve the equations.
We'll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application. 
When Aolani and her friends ate dinner at a restaurant, the bill came to  They wanted to leave a  tip. What amount would the tip be?
To solve this, we want to find what amount is  of  The  is called the base. The amount of the tip would be  or  See . To find the amount of the tip, we multiplied the percent by the base.
In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.
In the next examples, we are asked to find the base.
In the next examples, we will solve for the percent.

### Solve Applications of Percent

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.
We will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.
Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we'll solve involve everyday situations, you can rely on your own experience.

### Find Percent Increase and Percent Decrease

People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.
To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.
Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.

### Key Concepts

1. Solve an application.

2. Find percent increase.

3. Find percent decrease.


### Practice Makes Perfect

Translate and Solve Basic Percent Equations 
In the following exercises, translate and solve.
Solve Applications of Percents 
In the following exercises, solve the applications of percents.
Find Percent Increase and Percent Decrease 
In the following exercises, find the percent increase or percent decrease.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?
