Question

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?
(A) 25
(B) 34
(C) 55
(D) 70​

Answer 1

Answer:

25

Step-by-step explanation:

option no A

100 - 75 = 25

Answer 2

There were 85 students, and their scores were added up to a grand total, S.

So the average grade worked out to be S÷85, and it came up 85 points/student. So S=85^2=7225.

OK, we'll let x=number of students that earned 100

and y=number of students that earned 75.

Well, 100x + 75y = 7225 [the total number of points]

and x + y = 85 [the number of students in all]

So y = 85 - x

That means 100x + 75(85 - x) = 7225

Cleaning up gives us

100x - 75x + 6375 = 7225

then 25x = 7225 - 6375 = 950

So x = 950 ÷ 25 = 38

There you go.