Problem:
Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only of the problems she solved alone, but overall of her answers were correct. Zoe had correct answers to of the problems she solved alone. What was Zoe's overall percentage of correct answers?
Answer Choices:
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Solution:
For simplicity, suppose that the assignment contained problems. Chloe correctly solved of the problems she worked on alone, which was problems. She had a total of correct answers, so of the problems that she and Zoe worked on together had correct answers. In addition Zoe correctly solved of the problems that she worked on alone, which was problems. Her overall percentage of correct answers was .
Chloe's percentage of success on the half that she solved alone was , which is points less than . So her percentage of success on the other half was points above , or . Zoe's percentage of success was on half of the problems and on the other half, so her overall percentage was the average of and , which is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions