¶ 2008 AMC8 Problem 15
Problem:
In Theresa's first basketball games, she scored , and points. In her ninth game, she scored fewer than points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than points and her points-per-game average for the games was also an integer. What is the product of the number of points she scored in the ninth and tenth games?
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Solution:
The sum of the points Theresa scored in the first games is . After the ninth game, her point total must be a multiple of between and , inclusive. The only such point total is , so in the ninth game she scored points. Similarly, the next point total must be a multiple of between and . The only such point total is , so in the tenth game she scored points. The product of the number of points scored in Theresa's ninth and tenth games is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions