SOLUTION: There are 103 coins in all, totalling $15.25. How many quarters and how many dimes are there?

Question 106794: There are 103 coins in all, totalling $15.25. How many quarters and how many dimes are there?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Money problems involve your understanding both the number of coins and there value. The number of counts simply the count. To obtain the value, simply multiply by the number cents. So, if x is the number of quarters, then the value of the quarters is 25x.
Let q be the number of quarters, and let d be the number of dimes.
We know the value is: 25q + 10d = 1525. Note the total value is shown as 1525, not 15.25. 1525 is the value in cents.
We also know the number of coins is 103. So d = 103 - q.
Substituting, we have: 25q + 10(103-q) = 1525.
25q + 1030 - 10q = 1525.
Collecting like terms and then ubtracting 1030 from both sides, we have:
15q = 495.
Dividing by 15 we have: q = 33, so the number of quarters is 33.
That means the number of dimes is 103 - 33 = 70.
ALWAYS check.
33*25 +10*70 = 1525
825 + 700 = 1525.
1525 = 1525.
Check!
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