PSLE The number of girls and boys in a gymnasium were in the ratio 3 : 7. After 5 girls entered the gymnasium and half the number of boys left the gymnasium, the ratio of the number of girls to boys became 1 : 1. How many children were there in the gymnasium at first?
|
girls |
boys |
Total |
Before |
3 u |
7 u |
10 u |
Change |
+ 5 |
- 3.5 u |
|
After |
3 u + 5 |
3.5 u |
|
Number of boys who left the gymnasium
= 7 u ÷ 2
= 3.5 u
Number of girls in the end = 3 u + 5
Number of boys in the end = 3.5 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.
3.5 u = 3 u + 5
3.5 u - 3 u = 5
0.5 u = 5
1 u = 5 ÷ 0.5 = 10
Total number of children in the gymnasium at first
= 3 u + 7 u
= 10 u
= 10 x 10
= 100
Answer(s): 100