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?

$74$

$75$

$76$

$77$

$78$

Video solution:

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Written solution:

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 Problem 6

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Problem 6 in Other Years