PSLE The number of girls and boys in a auditorium were in the ratio 1 : 5. After 18 girls entered the auditorium and half the number of boys left the auditorium, the ratio of the number of girls to boys became 1 : 1. How many children were there in the auditorium at first?
|
girls |
boys |
Total |
Before |
1 u |
5 u |
6 u |
Change |
+ 18 |
- 2.5 u |
|
After |
1 u + 18 |
2.5 u |
|
Number of boys who left the auditorium
= 5 u ÷ 2
= 2.5 u
Number of girls in the end = 1 u + 18
Number of boys in the end = 2.5 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.
2.5 u = 1 u + 18
2.5 u - 1 u = 18
1.5 u = 18
1 u = 18 ÷ 1.5 = 12
Total number of children in the auditorium at first
= 1 u + 5 u
= 6 u
= 6 x 12
= 72
Answer(s): 72