AMC10 2021 B

AMC10 2021 B · Q6

AMC10 2021 B · Q6. It mainly tests Averages (mean), Weighted average.

Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is $84$, and the afternoon class's mean score is $70$. The ratio of the number of students in the morning class to the number of students in the afternoon class is $\frac{3}{4}$. What is the mean of the scores of all the students?

布莱克韦尔女士给两个班级的学生出了一场考试。上午班学生的成绩平均分为$84$，下午班的平均分为$70$。上午班学生人数与下午班学生人数之比为$\frac{3}{4}$。所有学生的成绩平均分是多少？

(A) 74 74

(B) 75 75

(D) 77 77

(E) 78 78

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let there be $3x$ students in the morning class and $4x$ students in the afternoon class. The total number of students is $3x + 4x = 7x$. The average is $\frac{3x\cdot84 + 4x\cdot70}{7x}=76$. Therefore, the answer is $\boxed{\textbf{(C)} ~76}$.

设上午班有$3x$名学生，下午班有$4x$名学生。总学生数为$3x + 4x = 7x$。平均分是$\frac{3x\cdot84 + 4x\cdot70}{7x}=76$。因此，答案是$\boxed{\textbf{(C)} ~76}$。

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