At first, the ratio of the number of girls to the number of boys at a park was 3 : 5. When 42 boys and some girls entered the park, the number of boys increased by 14% and the total number of children at the park increased by 35%.
- 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 |
(+ 126) |
+ 0.7 u (+ 42) |
+ 2.8 u (+ 168) |
3 u + 126 |
5.7 u |
10.8 u |
Number of boys that entered the park
= 14% x 5 u
=
14100 x 5 u
= 0.7 u
0.7 u = 42
1 u = 42 ÷ 0.7 = 60
Number of girls at first
= 3 u
= 3 x 60
= 180
(b)
Increase in the number of children
= 35% x 8 u
=
35100 x 8 u
= 2.8 u
Total number of children at the park in the end
= 8 u + 2.8 u
= 10.8 u
= 10.8 x 60
= 648
Increase in the number of girls
= 168 - 42
= 126
Total number of girls in the end
= 3 u + 126
= 3 x 60 + 126
= 306
Percentage of children who were girls
=
306648 x 100
= 47
29%
Answer(s): (a) 180; (b) 47
29%