PSLE
The number of boys and girls in a auditorium were in the ratio 2 : 7. After 6 boys entered the auditorium and half the number of girls left the auditorium, the ratio of the number of boys to girls became 1 : 1. How many children were there in the auditorium at first?

	boys	girls	Total
Before	2 u	7 u	9 u
Change	+ 6	- 3.5 u
After	2 u + 6	3.5 u

Number of girls who left the auditorium
= 7 u ÷ 2
= 3.5 u

Number of boys in the end = 2 u + 6
Number of girls in the end = 3.5 u

Since the ratio of the number of boys to girls in the end is 1 : 1, the number of boys and girls in the end is equal.

3.5 u = 2 u + 6
3.5 u - 2 u = 6
1.5 u = 6

1 u = 6 ÷ 1.5 = 4

Total number of children in the auditorium at first
= 2 u + 7 u
= 9 u
= 9 x 4
= 36

Answer(s): 36