### Instruction: The $\$4.55$ in Carol's piggy bank consists of quarters and nickels. There are seven more nickels than quarters. How many nickels does Carol have in her bank?### Response: This problem involves coins and their values, so I will use some algebra to represent the situation with equations.
Let q be the number of quarters and n be the number of nickels.
Each quarter is worth 25 cents, or 0.25 dollars, and each nickel is worth 5 cents, or 0.05 dollars.
The total value of the coins is 4.55 dollars, so I can write an equation for that: 0.25q + 0.05n = 4.55.
The problem also says that there are seven more nickels than quarters, so I can write another equation for that: n = q + 7.
Now I have a system of two equations with two variables, and I can use substitution to solve for one of them.
I will substitute n = q + 7 into the first equation and simplify: 0.25q + 0.05(q + 7) = 4.55.
Distributing the 0.05, I get 0.25q + 0.05q + 0.35 = 4.55.
Combining like terms, I get 0.3q + 0.35 = 4.55.
Subtracting 0.35 from both sides, I get 0.3q = 4.2.
Dividing both sides by 0.3, I get q = 14.
This means that Carol has 14 quarters in her piggy bank.
To find the number of nickels, I can use the second equation and plug in q = 14: n = 14 + 7.
Simplifying, I get n = 21.
This means that Carol has 21 nickels in her piggy bank.