PSLE The number of boys and girls in a gymnasium were in the ratio 4 : 9. After 3.5 boys entered the gymnasium and half the number of girls left the gymnasium, the ratio of the number of boys to girls became 1 : 1. How many children were there in the gymnasium at first?
|
boys |
girls |
Total |
Before |
4 u |
9 u |
13 u |
Change |
+ 3.5 |
- 4.5 u |
|
After |
4 u + 3.5 |
4.5 u |
|
Number of girls who left the gymnasium
= 9 u ÷ 2
= 4.5 u
Number of boys in the end = 4 u + 3.5
Number of girls in the end = 4.5 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.
4.5 u = 4 u + 3.5
4.5 u - 4 u = 3.5
0.5 u = 3.5
1 u = 3.5 ÷ 0.5 = 7
Total number of children in the gymnasium at first
= 4 u + 9 u
= 13 u
= 13 x 7
= 91
Answer(s): 91