In a college quiz, the boys averaged 68 points and the girls averaged 78 points; the overall average was 72. There were 12 more boys than girls. How many students took the quiz?

Explanation

1. 01

   Boys : girls = $(78 - 72) : (72 - 68) = 6 : 4 = 3 : 2$.

2. 02

   The difference of $3 - 2 = 1$ part is 12 students.

3. 03

   Total = $5 \times 12 = 60$ students (36 boys and 24 girls).