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?
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Solution:
To obtain the greatest possible amount of money, use as many nickels as possible: nickels and penny. This gives cents. Similarly, to obtain the least possible amount of money, use as many pennies as possible: nickel and pennies. This gives cents. Therefore the difference between the greatest possible and least possible amounts of money is cents.
One penny and one nickel will be used in either case so they can be removed, leaving coins. The greatest possible sum will result from having nickels, and the least possible sum will result from having pennies. The difference in amounts is cents.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions