Problem:
A charity sells benefit tickets for a total of . Some tickets sell for full price (a whole dollar amount), and the rest sell for half price. How much money is raised by the full-price tickets?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of full-price tickets and be the price of each in dollars. Then
Thus must be a factor of . Since , we have , and the only factor of that is in the required range for is . Therefore, , so and . The money raised by the full-price tickets is dollars.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions