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Question from hannah, a student:

i have 23.50 in quarters and dimes. if i have 15 more dimes than two times the amount of quarters i have, how many coins do i have total?

Hi Hannah,

Suppose I have D dimes and Q quarters. The total value is $23.50 or 2350¢. Thus

10 D + 25 Q = 2350

You have 15 more dimes then twice the number of quarters. Twice the number of quarters is 2Q so

2Q + 15 = D

Substitute this expression for D into the first equation to get

10 (2Q + 15) + 25 Q = 2350
20 Q + 150 + 25Q = 2350
45Q = 2350 - 250 = 2200

Q must be an integer but 45 does not divide 2200 so there is something wrong with this question.

Penny

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