Problem:
You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of , with at least one coin of each type. How many dimes must you have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since the total value is , you must have either or pennies. It is impossible to have pennies, since the two remaining coins cannot have a value of cents. With pennies the remaining coins have a value of . Either or of these must be quarters. If you have quarters, the other coins would be dimes, and you would have no nickels. The only possible solution is quarters, dime, nickels and pennies.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions