At first, the ratio of the number of girls to the number of boys at a concert hall was 3 : 5. When 60 boys and some girls entered the concert hall, the number of boys increased by 12% and the total number of children at the concert hall increased by 30%.
- How many girls were there at first?
- What percentage of the children at the concert hall were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
5 u |
8 u |
(+ 180) |
+ 0.6 u (+ 60) |
+ 2.4 u (+ 240) |
3 u + 180 |
5.6 u |
10.4 u |
Number of boys that entered the concert hall
= 12% x 5 u
=
12100 x 5 u
= 0.6 u
0.6 u = 60
1 u = 60 ÷ 0.6 = 100
Number of girls at first
= 3 u
= 3 x 100
= 300
(b)
Increase in the number of children
= 30% x 8 u
=
30100 x 8 u
= 2.4 u
Total number of children at the concert hall in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 100
= 1040
Increase in the number of girls
= 240 - 60
= 180
Total number of girls in the end
= 3 u + 180
= 3 x 100 + 180
= 480
Percentage of children who were girls
=
4801040 x 100
= 46
213%
Answer(s): (a) 300; (b) 46
213%