Math CentralQuandaries & Queries


Question from Leroy:

A total of 50 juniors and seniors were given a math test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

We have two responses for you

Hi Leroy,

The teacher added the scores of the 35 juniors and divided the total by 35. The result was 80. That is

(total of the junior's scores)/35 = 80

and thus

total of the junior's scores = 35 × 80

Can you see what to do now?


Hi Leroy.

The average score for all students would be the total of everyone's scores divided by the number of people.

The idea behind the question is this: The average is calculated by dividing the total score by the number of people, so if you know the average and the number of people, you can find the total score. Similarly, if you know the average and you know the total score, you can find the number of people. Thus, if you know any two of the three figures (total, average, people), you can determine the missing figure.

Figure 1: The number of people is 50.

Figure 2: The total of everyone's scores can be calculated. It is the total of the juniors' scores plus the total of the seniors' scores.

  1. The number of juniors times their average score is the total of the juniors' scores.

  2. The seniors' total is calculated the same way.

Fact 3: Since you know the number of people (Figure 1) and the total score (Figure 2), you can divide to find the average overall score.

Hope this helps,
Stephen La Rocque.

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