AMC10 2021 A

AMC10 2021 A · Q5

AMC10 2021 A · Q5. It mainly tests Linear equations, Averages (mean).

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 $k$?

一个有$k > 12$名学生的班级的测验分数平均分为$8$。其中$12$个分数平均分为$14$。其余分数的平均分用$k$表示是多少？

(A) \frac{14-8}{k-12} \frac{14-8}{k-12}

(B) \frac{8k-168}{k-12} \frac{8k-168}{k-12}

(D) \frac{14(k-12)}{k^2} \frac{14(k-12)}{k^2}

(E) \frac{14(k-12)}{8k} \frac{14(k-12)}{8k}

Answer

Correct choice: (B)

正确答案：（B）

Solution

The total score of the class is $8k,$ and the total score of the $12$ quizzes is $12\cdot14=168.$ Therefore, for the remaining quizzes ($k-12$ of them), the total score is $8k-168.$ Their mean score is $\boxed{\textbf{(B)} ~\frac{8k-168}{k-12}}.$

班级总分为$8k$，$12$个测验总分为$12\cdot14=168$。因此，其余$k-12$个测验的总分为$8k-168$。它们的平均分为 $\boxed{\textbf{(B)} ~\frac{8k-168}{k-12}}$。

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