PSLE
The number of girls and boys in a auditorium were in the ratio 2 : 7. After 10.5 girls entered the auditorium and half the number of boys left the auditorium, the ratio of the number of girls to boys became 1 : 1. How many children were there in the auditorium at first?

	girls	boys	Total
Before	2 u	7 u	9 u
Change	+ 10.5	- 3.5 u
After	2 u + 10.5	3.5 u

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

Number of girls in the end = 2 u + 10.5
Number of boys in the end = 3.5 u

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

3.5 u = 2 u + 10.5
3.5 u - 2 u = 10.5
1.5 u = 10.5

1 u = 10.5 ÷ 1.5 = 7

Total number of children in the auditorium at first
= 2 u + 7 u
= 9 u
= 9 x 7
= 63

Answer(s): 63