2021 AMC 10B Spring Problem 6

Question

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

Use

3x

and

4x

students for the two classes

Compute the weighted average from the two total score sums

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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 .

Problem 6 in other years