PSLE The number of boys and girls in a auditorium were in the ratio 2 : 7. After 16.5 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 |
2 u |
7 u |
9 u |
Change |
+ 16.5 |
- 3.5 u |
|
After |
2 u + 16.5 |
3.5 u |
|
Number of girls who left the auditorium
= 7 u ÷ 2
= 3.5 u
Number of boys in the end = 2 u + 16.5
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 + 16.5
3.5 u - 2 u = 16.5
1.5 u = 16.5
1 u = 16.5 ÷ 1.5 = 11
Total number of children in the auditorium at first
= 2 u + 7 u
= 9 u
= 9 x 11
= 99
Answer(s): 99