Question

A mix of 32 quarters and dimes totals $6.35. Find the system of equations that would help you answer the question and then find how many quarters (x) and dimes (y) you would have?

Answer 1

21 quarters and 11 dimes = 32 coins

Explanation:

x + y = 32

0.25x + 0.10y = 6.35 [take the first equation and make it equal to x]

x = 32 - y [now take this equation and plug it in the above]

0.25 (32-y) + 0.10y = 6.35

8 - 0.25y + 0.10y = 6.35

8 - 0.15y = 6.35 [subtract 8 from both sides]

-0.15y = -1.65 [divide by -0.15 to isolate y]

y = 11 so there are 11 dimes

plug it into the first equation: x + 11 = 32; x = 21 so there are 21 quarters