PSLE The number of boys and girls in a auditorium were in the ratio 1 : 3. After 8 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 |
3 u |
4 u |
Change |
+ 8 |
- 1.5 u |
|
After |
1 u + 8 |
1.5 u |
|
Number of girls who left the auditorium
= 3 u ÷ 2
= 1.5 u
Number of boys in the end = 1 u + 8
Number of girls in the end = 1.5 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.
1.5 u = 1 u + 8
1.5 u - 1 u = 8
0.5 u = 8
1 u = 8 ÷ 0.5 = 16
Total number of children in the auditorium at first
= 1 u + 3 u
= 4 u
= 4 x 16
= 64
Answer(s): 64