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?


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 = {{{850/25}}}, or {{{highlight_green(34)}}}


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