Question

You have a total of 52 dimes and quarters. You have 10 more quarters than dimes. Which system of

equations can you use to find the number z of quarters and number y of dimes you have? Use the system to
determine how much money you have in quarters and dimes.

Answer 1

9514 1404 393

Answer:

z + y = 52; z - y = 10; z = 31; y = 21; $9.85 total

Explanation:

The variables are defined in the problem statement. The equations could be ...

z + y = 52 . . . . . . total number of coins

z - y = 10 . . . . . . . 10 more quarters than dimes

These equations can be solved by adding them together.

(z +y) +(z -y) = (52) + (10)

2z = 62 . . . . . . . simplify

z = 31 . . . . . . . . . divide by 2

31 -10 = y = 21 . . . . find the number of dimes

There are 31 quarters and 21 dimes.

The value of the coins is ...

31($0.25) +21($0.10) = $7.75 +2.10 = $9.85