PSLE The number of boys and girls in a auditorium were in the ratio 1 : 5. After 22.5 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 |
1 u |
5 u |
6 u |
Change |
+ 22.5 |
- 2.5 u |
|
After |
1 u + 22.5 |
2.5 u |
|
Number of girls who left the auditorium
= 5 u ÷ 2
= 2.5 u
Number of boys in the end = 1 u + 22.5
Number of girls in the end = 2.5 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.
2.5 u = 1 u + 22.5
2.5 u - 1 u = 22.5
1.5 u = 22.5
1 u = 22.5 ÷ 1.5 = 15
Total number of children in the auditorium at first
= 1 u + 5 u
= 6 u
= 6 x 15
= 90
Answer(s): 90