Question 28831
these are formulas for averages
(total of juniors scores) / 35 = 80
(total of seniors scores) / 15 = 70
cross-multiply each equation
[1] total of juniors scores = 35*80
[2] total of seniors scores = 15*70
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this is the formula for the whole group average
(total of scores for both juniors and seniors) / 50 = average score
substituting [1] & [2] from above
average score = (35*80 + 15*70) / 50
divide top & bottom by 5
average score = (7*80 + 3*70) / 10
divide top & bottom by 10
average score = (7*8 + 3*7) / 1
average score = 56 + 21 = 77
this makes sense, because since more got 80, the average would be
shifted toward them