AMC8 2017

AMC8 2017 · Q14

AMC8 2017 · Q14. It mainly tests Linear equations, Averages (mean).

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?

Chloe和Zoe都是Ms. Demeanor数学课的学生。昨晚她们各自独立完成了作业的一半，然后一起完成了另一半。Chloe独立完成的题目正确率为80%，但总体正确率为88%。Zoe独立完成的题目正确率为90%。Zoe的总体正确率是多少？

(A) 89 89

(B) 92 92

(D) 96 96

(E) 98 98

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): For simplicity, suppose that the assignment contained 100 problems. Chloe correctly solved 80% of the 50 problems she worked on alone, which was 40 problems. She had a total of 88 correct answers, so 88-40 = 48 of the 50 problems that she and Zoe worked on together had correct answers. In addition Zoe correctly solved 90% of the 50 problems that she worked on alone, which was 45 problems. Her overall percentage of correct answers was 45 + 48 = 93.

答案（C）：为简便起见，设这份作业共有 100 道题。Chloe 独立完成的 50 道题中，她做对了 80%，也就是 40 题。她总共答对了 88 题，所以她与 Zoe 一起完成的那 50 道题中，有 88-40 = 48 题答对。另外，Zoe 独立完成的 50 道题中，她做对了 90%，也就是 45 题。她的总体正确率是 45 + 48 = 93。

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