Jamie has a collection of 78 nickels, dimes, and quarters worth $12.40. if the number of quarters is
doubled, the value becomes $22.15. how many of each type of coin does jamie have?

9514 1404 393

Step-by-step explanation:

Doubling the number of quarters increases the value by ...

  22.15 -12.40 = 9.75 = 39×0.25

The number of quarters is 39, which means the number of nickels and dimes is 78 -39 = 39, and their value is ...

  12.40 -9.75 = 2.65

Let d represent the number of dimes. Then 39-d is the number of nickels and we have ...

  0.05(39 -d) +0.10(d) = 2.65

  0.05d + 1.95 = 2.65 . . . . simplify

  0.05d = 0.70 . . . . . . . . . . subtract 1.95

  d = 14

  39 -d = 25

Jamie has 25 nickels, 14 dimes, and 39 quarters in the collection.

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