PSLE
The number of girls and boys in a auditorium were in the ratio 1 : 3. After 4.5 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	1 u	3 u	4 u
Change	+ 4.5	- 1.5 u
After	1 u + 4.5	1.5 u

Number of boys who left the auditorium
= 3 u ÷ 2
= 1.5 u

Number of girls in the end = 1 u + 4.5
Number of boys in the end = 1.5 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.

1.5 u = 1 u + 4.5
1.5 u - 1 u = 4.5
0.5 u = 4.5

1 u = 4.5 ÷ 0.5 = 9

Total number of children in the auditorium at first
= 1 u + 3 u
= 4 u
= 4 x 9
= 36

Answer(s): 36