Problem:
The Amaco Middle School bookstore sells pencils costing a whole number of cents. Some seventh graders each bought a pencil, paying a total of . Some of the sixth graders each bought a pencil, and they paid a total of . How many more sixth graders than seventh graders bought a pencil?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The number of sixth graders who bought a pencil is divided by the cost of a pencil. Similarly the number of seventh graders who bought a pencil is divided by the cost of a pencil. That means both and are multiples of the price of the pencil. Factor and . The only common divisors are and . If a pencil cost cent, then sixth graders bought a pencil. However, there are only sixth graders, so a pencil must cost cents. Using that fact, more sixth graders than seventh graders bought pencils.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions