Question

Joe has a total of 14 pennies, dimes and quarters in his pocket, which total $1.52. The number of dimes and quarters combined is equal to the number of pennies. How many of each coin does Joe have?

Please show your work so I can see how you did it. Thanks!

Answer 1

We can solve this using algebra by setting up a couple of equations.
\[
p=\text{pennies}, d=\text{dimes}, q=\text{quarters}\\
p+d+q=14\\
p+10d+25q=152\\
\]Now you can solve that system of equations. The easiest way for this problem, though, is to use a version of guess-and-check. We know there are less than 7 quarters, because that would be $1.75. So we can work our way down from there and check each option. If there are 6 quarters, then it's 6 quarters and 2 pennies, which is only 8 coins. 5 quarters, then we need 5 quarters, 2 dimes, 7 pennies, which is 14 coins, and there's our answer.