Problem:
Ricardo has coins, some of which are pennies ( coins) and the rest of which are nickels ( coins). He has at least one penny and at least one nickel. What is the difference in cents between the greatest possible and least possible amounts of money that Ricardo can have?
Answer Choices:
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B.
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E.
Solution:
Let be the number of pennies Ricardo has and let be the number of nickels he has. We know that , and , (by the problem statement). This means , so .
It follows, then, that Ricardo has cents. Therefore, to maximize the money he has, we maximize the number of nickels he has, and minimizing the money he has involves minimizing the number of nickels he has.
The maximum number of nickels he can have is , so he can have at most cents. The minimum number of nickels he can have is , so he has at most cents.
The difference between the maximum and minimum amount of money he can have is
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions