Averages question... please help

Question

A class of 20 boys and 30 girls take a test.

The mean for the class is 56.

The mean for the girls is 60.

What is the mean for the boys?

 

Answer 1

20+30=50 total students

50*56=2800 total points

30*60=1800 total points for girls

2800-1800=1000 total points for boys

1000/20=50 mean for boys

Answer 2

Let G represent the sum of all the girls' grades. Let B represent the sum of all the boys' grades. Then G+B is the sum of the grades for the girls and boys. Keep in mind that there are 30+20=50 total students in the class.

 

Then if the mean for the class is 56, we know that (G+B)/50=56. Since the mean for the girls is 60, we know that G/30=60. Working with this last equation and solving for G we multiply by 30 on each side to get G=1800.

 

Now let's substitute this in for the first equation. We get (1800+B)/50=56. Multiplying each side by 50 we get 1800+B=2800. Subtracting 1800 from each side we get B=1000. So the sum of the boys' grades is 1000.

 

The average is then 1000/20=50