At first, the ratio of the number of girls to the number of boys at a park was 3 : 5. When 56 boys and some girls entered the park, the number of boys increased by 16% and the total number of children at the park increased by 30%.
- How many girls were there at first?
- What percentage of the children at the park were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
5 u |
8 u |
(+ 112) |
+ 0.8 u (+ 56) |
+ 2.4 u (+ 168) |
3 u + 112 |
5.8 u |
10.4 u |
Number of boys that entered the park
= 16% x 5 u
=
16100 x 5 u
= 0.8 u
0.8 u = 56
1 u = 56 ÷ 0.8 = 70
Number of girls at first
= 3 u
= 3 x 70
= 210
(b)
Increase in the number of children
= 30% x 8 u
=
30100 x 8 u
= 2.4 u
Total number of children at the park in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 70
= 728
Increase in the number of girls
= 168 - 56
= 112
Total number of girls in the end
= 3 u + 112
= 3 x 70 + 112
= 322
Percentage of children who were girls
=
322728 x 100
= 44
313%
Answer(s): (a) 210; (b) 44
313%