Question

A box contains 81 coins, only dimes and nickels. The amount of money in the box is $5.30. How many dimes and how many nickels are in the box?
The number of dimes is
The number of nickels is

Answer 1

Answer:

• 25 dimes
• 56 nickels

Step-by-step explanation:

Let d represent the number of dimes. Then 81-d is the number of nickels and the total value in cents is ...

  10d +5(81-d) = 530

  5d +405 = 530 . . . eliminate parentheses

  d +81 = 106 . . . . . divide by 5

  d = 25 . . . . . . . . . subtract 81; number of dimes

  81 -d = 81 -25 = 56 . . . . . number of nickels

There are 25 dimes and 56 nickels in the box.

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Comment on the method of solution

It usually works well to let the variable represent the amount of the highest-value contributor (dimes). This keeps the numbers positive as the solution progresses.