How Many Dimes?

How Many Dimes?
A woman has \$2.15 in change in her purse, made up entirely of dimes and quarters. Given that there are more quarters than dimes in her purse, what is the total number of dimes?
Source: NCTM Mathematics Teacher, November 2006

SOLUTION
Let q be the number of quarters and d the number of dimes.
25q+10d=215
10d=215-25q
=5(43-5q)
Simplify
2d=43-5q\qquad (1)
Since 2d is even, 43-5q is even which implies that q is odd.
If q=9, 9q=225 > 215
If q=7, 7q=175 < 215
Substitute the value of q into Eq.(1)
2d=43-5(7)=8
d=4
If q=5, Eq. (1) is also satisfied but with 9 dimes.
The total number of dimes equals 4.

Answer: 4 dimes

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About mvtrinh

Retired high school math teacher.
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