Question

You have quarters and dimes that total $2.80. Your friend says it is possible that the number of quarters is 8 more than the number of dimes. Is your friend correct? Explain. Let d represent the number of dimes.

Answer 1

No.

Explanation:

Let d represent the number of dimes. Then the number of quarters (according to the friend) is d+8. The total value is

... 10d +25(d+8) = 280 . . . . in cents

... 35d + 200 = 280 . . . . . . eliminate parentheses

... 35d = 80 . . . . . . . . . . . . . subtract 200

... d = 80/35 = 16/7 = 2 1/7 . . . . . not a realistic number of coins

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The difference between the number of quarters and the number of dimes may be any multiple of 7.