Question

Assume that advanced students average 93% on an achievement test and regular students averaged 75%. If 100 advanced students and 300 regular students took the test, what would you expect the average to be? How many of each kind of student would be needed to get a group of 90 students who average 87% on the test? Please include work/explaination, I along with a few of my classmates are confused by this problem. We are in a chapter about systems of equations.

Answer 1

Average (mean) = (sum of all the data) / (# of data)

sum of all the data = (average)(# of data)

Thus for 100 students with an average of 93,
sum of all data = (93)(100) = 9300

and for 300 students with an average of 75,
sum of all data = (75)(300) = 22500

Therefore you would expect the overall average to be
(9300 + 22500) / (100 + 300) = 79.5 %

Now if there are x # of advanced students and y # of regular students, then

x + y = 90 (total # of students) and 93x + 75y = 87(x + y) (overall average)

The second equation can be simplified to x - 2y = 0

Subtracting the two equations yields

x = 60 and y = 90

Therefore you would need 60 advanced and 30 regular students.