AMC10 2007 B

AMC10 2007 B · Q16

AMC10 2007 B · Q16. 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出了一次测试，班级中有10%的学生是低年级生，90%是高年级生。测试的平均分为84。所有低年级生的得分相同，高年级生的平均分为83。低年级生每人得了多少分？

(A) 85 85

(B) 88 88

(D) 94 94

(E) 98 98

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Let $N$ be the number of students in the class. Then there are $0.1N$ juniors and $0.9N$ seniors. Let $s$ be the score of each junior. The scores totaled $84N = 83(0.9N) + s(0.1N)$, so $s = \dfrac{84N - 83(0.9N)}{0.1N} = 93.$ Note: In this problem, we could assume that the class has one junior and nine seniors. Then $9\cdot 83 + s = 10\cdot 84 = 9\cdot 84 + 84$ and $s = 9(84 - 83) + 84 = 93.$

答案（C）：设$N$为班级学生人数，则有$0.1N$名低年级生（junior）和$0.9N$名高年级生（senior）。设每个低年级生的分数为$s$。总分为$84N = 83(0.9N) + s(0.1N)$，因此 $s = \dfrac{84N - 83(0.9N)}{0.1N} = 93。$ 注：本题也可以假设班里有1名低年级生和9名高年级生。则 $9\cdot 83 + s = 10\cdot 84 = 9\cdot 84 + 84$，并且$s = 9(84 - 83) + 84 = 93。$

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