A total of 80 pupils take part in a mathematics test and the average score was 69 marks. Given the average score of the boys was 75 marks and the average score for the girls was 65 marks. find the number of boys who took the test.

Answer 1

b boys, 80-b girls
Now add up the total points scored:
75(b) + 65(80-b) = 69(80)

Answer 2

Fast method:
Ratio of boys to girls
= (69-65):(75-69)
=4:6
=2:3
Number of boys = 80*2/(2+3) = 32

Standard method:
Let x=number of boys
(75*x + 65*(80-x))/80 = 69
Solve for x
75x-65x = 69*80-5200 = 320
10x=320
x=32
Answer: there are 32 boys.