In a class, the boys' average score is 72 and the girls' average score is 80. The class average is 77. What is the ratio of the number of boys to the number of girls?

Explanation

1. 01

   Boys are $77 - 72 = 5$ below the class average; girls are $80 - 77 = 3$ above it.

2. 02

   The totals balance, so boys × 5 = girls × 3.

3. 03

   Boys : girls = $3 : 5$.

4. 04

   Check with 3 boys and 5 girls: $\frac{3 \times 72 + 5 \times 80}{8} = \frac{616}{8} = 77$.