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Question

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 80% of the problems she solved alone, but overall 88% of her answers were correct. Zoe had correct answers to 90% of the problems she solved alone. What was Zoe's overall percentage of correct answers?

Accepted Answer

Let the number of questions that they solved alone be x. Let the percentage of problems they correctly solve together be a%. As given, 80x100 + ax100 = 2 88x100. Hence, a = 96. Zoe got 90x100 + ax100 = 186x100 problems right out of 2x. Therefore, Zoe got 186x1002x = 93100 = 93 percent of the problems correct.