Ajar holding 36 coins, only nickels and quarters, is worth $6.20. There are eight more quarters than there are nickels. How many nickels are in the jar?

  14

Step-by-step explanation:

Let n represent the number of nickels. Then the number of quarters is 36-n. The difference is ...

  (36-n) -n = 8 . . . . . 8 more quarters than nickels

  18 -n = 4 . . . . . . . divide by 2

  14 = n . . . . . . . . add n-4 to both sides

There are 14 nickels in the jar.

_____

Additional comment

The problem supplies more information than is needed for a solution. You can work this as a "sum and difference" problem, as we have above, or you can work it as a "mixture" problem where the total coin value comes into play. Any two of the three given relations will give a solution.

  n + q = 36 . . . . . . . number of coins

  5n +25q = 620 . . . value of coins (in cents)

  q -n = 8 . . . . . . . . difference in number of coins

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