SOLUTION: On a certain project the only grades awarded were 75 and 100.If 85 students completed the project and the average of their grades was 85,how many earned 100?

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Question 623461: On a certain project the only grades awarded were 75 and 100.If 85 students completed the project and the average of their grades was 85,how many earned 100?
Answer by MathTherapy(10552) About Me  (Show Source):
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On a certain project the only grades awarded were 75 and 100.If 85 students completed the project and the average of their grades was 85,how many earned 100?

Eighty-five students with an average of 85 means that their total score is 7,225 (85 * 85)

Let the amount of students who received grades of 75 and 100 be S and H, respectively

Then S + H = 85 ------ S = 85 – H ------ eq (i)
Also, 75S + 100H = 7,225 ------ eq (ii)
75(85 – H) + 100H = 7,225 ------- Substituting 85 – H for S in eq (ii)
6,375 – 75H + 100H = 7,225
6,375 + 25H = 7,225
25H = 7,225 – 6,375
25H = 850
H, or amount of students who received hundreds = 850%2F25, or highlight_green%2834%29

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