Problem:
Steph scored baskets out of attempts in the first half of a game, and baskets out of attempts in the second half. Candace took attempts in the first half and attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?
Answer Choices:
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Solution:
They both shot baskets total, so if they have the same make percentage, then they made the same total amount. This means Candace also made total shots. Now, let be the number of shots Candace made in the first half and let be the number of shots Candace made in the second half. We know she made shots, so . By the condition that she had a lower percentage in each half, we know and . With cross multiplication, we know and . Since and are whole numbers, we have the restrictions that and . With our knowledge that and the conditions that and , the only possible solution is and . This makes our answer .
Thus, the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions