At Jefferson School, both 6th grade and 7th grade classes took a math test. The average score for the 6th grade is 80 and for the 7th grade is 90. If there are twice as many students in the 7th grade as that in the 6th grade, what is the average test score for both grades together?

Answer 1

Suppose we let
x = # 6th graders
Then 2x = # 7th graders
Now find the average of all the students:
(80x + 90*2x)/(x+2x) = (80x+180x)/3x = 260/3 = 86.6

Just FYI, note that since 2/3 of the students are 7th graders, the total average is 2/3 of the way from 80 to 90.