2021 AMC 12B Spring Problem 4

Below is the professionally curated solution for Problem 4 of the 2021 AMC 12B Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Spring solutions, or check the answer key.

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Concepts:mean ratio and proportion

Difficulty rating: 1100

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 $\dfrac{3}{4}.$ What is the mean of the scores of all the students?

$74$

$75$

$76$

$77$

$78$

Solution:

Suppose there are $3$ students in the morning class and $4$ in the afternoon class.

The total of all scores is $3\cdot 84+4\cdot 70=252+280=532.$

The overall mean is $\dfrac{532}{7}=76.$

Thus, the correct answer is C.

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