¶ 2014 AMC8 Problem 2
Problem:
Paul owes Paula cents and has a pocket full of -cent coins, -cent coins, and -cent coins that he can use to pay her. What is the difference between the largest and the smallest number of coins he can use to pay her?
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Solution:
To use the largest number of coins, Paul would use only -cent coins. Because , the largest number of coins Paul can use is . To use the smallest number of coins, Paul would use a -cent coin and a -cent coin, for a total of coins. The difference between the largest and the smallest number of coins he can use is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions