Three times as many girls as boys attend a class. If the girls average 18 points and the class average is 17 points, how many points does each boy score on average?

• A. 15 points
• B. 18 points
• C. 14 points
• D. 17 points

Answer: (C)

The idea is to use a weighted average. If there are three times as many girls as boys, let the number of boys be b and the number of girls be 3b. The total score is 3b times 18 plus b times the boys’ average. The overall average is 17, so the total score equals 4b times 17.

Set up the equation: 3b × 18 + b × (boys’ average) = 4b × 17.

That’s 54b + b × (boys’ average) = 68b. Subtract 54b from both sides: b × (boys’ average) = 14b, so the boys’ average is 14.

Checking: total score = 3b×18 + b×14 = 54b + 14b = 68b, and 68b ÷ 4b = 17, which matches the class average. The other numbers would not produce the required overall average.