SOLUTION: A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the averag

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Let x=sum of the group who scored an average of 80
and y=sum of the group who scored an average of 70

First lets find the sum of the 35 junior's test scores who scored an average of 80
Start with the given average

Multiply both sides by 35

So the sum of the group who scored an average of 80 is 2,800


Now lets find the sum of the 15 junior's test scores who scored an average of 70

Start with the given average

Multiply both sides by 15

So the sum of the group who scored an average of 70 is 1,050


Now lets average the 2 groups:



So the average score for all 50 is 77