AMC12 2007 B

AMC12 2007 B · Q12

AMC12 2007 B · Q12. It mainly tests Averages (mean), Weighted average.

A teacher gave a test to a class in which $10\%$ of the students are juniors and $90\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on the test?

一位老师给一个班级进行了一次测试，其中 $10\%$ 的学生是低年级生，$90\%$ 是高年级生。测试的平均分是 $84.$ 所有低年级生的得分都相同，而高年级生的平均分是 $83.$ 问每个低年级生在测试中得了多少分？

(A) 85 85

(B) 88 88

(D) 94 94

(E) 98 98

Answer

Correct choice: (C)

正确答案：（C）

Solution

We can assume there are $10$ people in the class. Then there will be $1$ junior and $9$ seniors. The sum of everyone's scores is $10 \cdot 84 = 840$. Since the average score of the seniors was $83$, the sum of all the senior's scores is $9 \cdot 83 = 747$. The only score that has not been added to that is the junior's score, which is $840 - 747 = \boxed{\textbf{(C) } 93}$

我们可以假设班里有 $10$ 个人。则有 $1$ 个低年级生和 $9$ 个高年级生。全班总分为 $10 \cdot 84 = 840$。由于高年级生的平均分为 $83$，所有高年级生的总分为 $9 \cdot 83 = 747$。剩下未计入的就是低年级生的分数，因此为 $840 - 747 = \boxed{\textbf{(C) } 93}$

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