2021 AMC 10A Spring 第 5 题

Question

一个有

k > 12

名学生的班级，测验分数的平均数为

8

。其中

12

个测验分数的平均数为

14

。其余测验分数的平均数用

k

表示是多少？

The quiz scores of a class with

k > 12

students have a mean of

8.

The mean of a collection of

12

of these quiz scores is

14.

What is the mean of the remaining quiz scores in terms of

k?

\dfrac{14-8}{k-12}

\dfrac{8k-168}{k-12}

\dfrac{14}{12} - \dfrac{8}{k}

\dfrac{14(k-12)}{k^2}

\dfrac{14(k-12)}{8k}

把每个平均数都转化为总分。

Convert each mean into a total score

从全班总分中减去那

12

个分数的总分。

Subtract the known total for the chosen

12

scores from the class total

Click to load, then click again to play

全班所有人的总分为

8k

。这

12

个分数的总分为

12 \cdot 14 = 168

。

其余学生的总分为

8k - 168

，人数为

k - 12

。因此平均数为

\dfrac{8k - 168}{k - 12}\text{。}

所以正确答案是 B。

The sum of the scores of everyone in the class is

8k.

The sum of the scores in the collection of

12

is

12 \cdot 14 = 168.

This means that the sum of the scores of everyone not in the collection is

8k - 168.

There are also

k - 12

people not in the collection. Therefore, the average is

\dfrac{8k - 168}{k - 12}.

Thus, B is the correct answer.

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