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?

$89$

$92$

$93$

$96$

$98$

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Written solution:

Since the answer is the same regardless of the number of problems, we can assume that there were $100$ problems on the assignment. $80\%$ of $50$ is $40,$ so Chloe answered $40$ questions correctly alone. $88\%$ of $100$ is $88,$ so Chloe answered $88$ questions correctly in total. This means that Chloe answered $88 - 40 = 48$ together with Zoe.

$90\%$ of $50$ is $45,$ so Zoe answered $45$ questions correctly by herself. We know that she answered $48$ questions correctly with Chloe, so she answered $45 + 48 = 93$ correctly in total. This means that her overall percentage is $93\%.$

Thus, C is the correct answer.

2017 AMC 8 Problem 14

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Problem 14 in Other Years