Problem:
The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse?
Answer Choices:
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Solution:
If is the number of coins in Paula's purse, then their total value is cents. If she had one more quarter, she would have coins whose total value in cents could be expressed both as and as . Therefore
Since Paula has four coins with a total value of 80 cents, she must have three quarters and one nickel, so the number of dimes is .
The problems on this page are the property of the MAA's American Mathematics Competitions