Question

Sang Jin has only quarters and nickels in her piggy bank. She has 66 coins in the bank with a value of $11.50.

How many quarters are in Sang Jin’s piggy bank?

Answer 1

First you pick two variables, and you state what they stand for:
Let x = number of quarters
Let y = number of nickels

The total number of coins is 66, so that gives us our first equation:

x + y = 66


Now you work with the values of the coins.
A quarter is worth $0.25, so x quarters are worth 0.25x
A nickel is worth $0.05, so y nickels are worth 0.05y.

The total value of the coins is $11.50, so you add their values and set that equal to $11.50.

0.25x + 0.05y = 11.50

That is the second equation.

Now you have this system of equations that you need to solve:

x + y = 66
0.25x + 0.05y = 11.5

Answer 2

Your answer is 41 quarters.