At first, the ratio of the number of girls to the number of boys at a stadium was 3 : 7. When 56 boys and some girls entered the stadium, the number of boys increased by 10% and the total number of children at the stadium increased by 26%.
- How many girls were there at first?
- What percentage of the children at the stadium were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
7 u |
10 u |
(+ 152) |
+ 0.7 u (+ 56) |
+ 2.6 u (+ 208) |
3 u + 152 |
7.7 u |
12.6 u |
Number of boys that entered the stadium
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 56
1 u = 56 ÷ 0.7 = 80
Number of girls at first
= 3 u
= 3 x 80
= 240
(b)
Increase in the number of children
= 26% x 10 u
=
26100 x 10 u
= 2.6 u
Total number of children at the stadium in the end
= 10 u + 2.6 u
= 12.6 u
= 12.6 x 80
= 1008
Increase in the number of girls
= 208 - 56
= 152
Total number of girls in the end
= 3 u + 152
= 3 x 80 + 152
= 392
Percentage of children who were girls
=
3921008 x 100
= 38
89%
Answer(s): (a) 240; (b) 38
89%