2021 AMC 12B Problem 4

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?

Show solution

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.

Tagged: mean · ratio and proportion