Question

Chloe 和 Zoe 都是 Demeanor 女士数学课上的学生。昨晚她们各自独立完成了家庭作业的一半题目，然后一起完成了另一半。Chloe 独立完成的题中只有 $80\%$ 正确，但总体有 $88\%$ 的答案正确。Zoe 独立完成的题中 $90\%$ 正确。Zoe 的总体正确率是多少？

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?

$89$

$92$

$93$

$96$

$98$

答案：C

知识点：百分数

难度评级：1370

视频讲解：

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文字解答：

因为题目数量不影响答案，可以假设作业有 $100$ 道题。 $80\%$ 的 $50$ 是 $40$ ，所以 Chloe 独立答对 $40$ 道。 $88\%$ 的 $100$ 是 $88$ ，所以 Chloe 总共答对 $88$ 道。因此共同完成部分她答对 $88 - 40 = 48$ 道。

$90\%$ 的 $50$ 是 $45$ ，所以 Zoe 独立答对 $45$ 道。共同完成部分她也答对 $48$ 道，所以总共答对 $45 + 48 = 93$ 道，整体正确率为 $93\%$ 。

所以正确答案是 C。

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 第 14 题

答案：C

难度评级：1370

视频讲解：

文字解答：

其他年份的第 14 题