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

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.

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.

if x = 1, then the answer is 3.5

so, converting firstly the mixed fractions to improper fractions and then "adding".