Problem:
A majority of the students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than . The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was . What was the cost of a pencil in cents?
Answer Choices:
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Solution:
Let be the cost of a pencil in cents, be the number of pencils each student bought, and be the number of students who bought pencils. Then , and . Because a majority of the students bought pencils, . Therefore , and .
The problems on this page are the property of the MAA's American Mathematics Competitions