Question

Blackwell 老师给两个班考试。上午班学生的平均分是 $84$ ，下午班学生的平均分是 $70$ 。上午班人数与下午班人数之比为 $\frac{3}{4}$ 。所有学生的平均分是多少？

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?

$74$

$75$

$76$

$77$

$78$

答案：C

知识点：平均数比与比例

难度评级：900

视频讲解：

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文字解答：

设上午班有 $3x$ 人，那么下午班有 $4x$ 人。

上午班总分为 $84\cdot 3x = 252x$ ，下午班总分为 $70\cdot 4x = 280x$ 。因此总分为 $532x$ 总人数为 $7x$ 。

所以所有学生的平均分为 $\dfrac{532x}{7x} = 76$ 。

所以正确答案是 C。

Let the number of people in the first class be $3x.$ This means the number of people in the second class is $4x.$

Thus, the sum of the scores of the first class is $84\cdot 3x = 252x$ and the sum of the scores for the people in the second class is $70\cdot 4x = 280x.$ This means the total sum is $532x,$ with $7x$ people.

Therefore, the average of all the students is $\dfrac{532x}{7x} = 76.$

Thus, the correct answer is C .

2021 AMC 10B Spring 第 6 题

答案：C

难度评级：900

视频讲解：

文字解答：

其他年份的第 6 题