In a science class, there are twice as many boys as girls. If the girls average 90 points and the class average is 80 points, what is the average score of the boys?

In a science class, there are twice as many boys as girls. If the girls average 90 points and the class average is 80 points, what is the average score of the boys?

• A. 75
• B. 80
• C. 70
• D. 85

Answer: (A)

Weighted averages are at work here: the overall class score comes from combining the two groups in proportion to how many students are in each. If there are g girls and twice as many boys, there are 2g boys, for a total of 3g students. The girls contribute 90g points in total. Let the boys’ average be b; their total contribution is 2gb. The class average is the total points divided by total students, so (90g + 2gb) / (3g) = 80. Simplifying, (90 + 2b)/3 = 80, so 90 + 2b = 240, which gives 2b = 150 and b = 75. So the boys average 75. If you test nearby values, you’ll see that 80 would push the class average above 80, 70 would pull it below, and 85 would raise it even more, so 75 fits exactly.

Weighted averages are at work here: the overall class score comes from combining the two groups in proportion to how many students are in each. If there are g girls and twice as many boys, there are 2g boys, for a total of 3g students. The girls contribute 90g points in total. Let the boys’ average be b; their total contribution is 2gb. The class average is the total points divided by total students, so (90g + 2gb) / (3g) = 80. Simplifying, (90 + 2b)/3 = 80, so 90 + 2b = 240, which gives 2b = 150 and b = 75. So the boys average 75. If you test nearby values, you’ll see that 80 would push the class average above 80, 70 would pull it below, and 85 would raise it even more, so 75 fits exactly.