At first, the ratio of the number of girls to the number of boys at a safari park was 3 : 7. When 42 boys and some girls entered the safari park, the number of boys increased by 15% and the total number of children at the safari park increased by 26%.
- How many girls were there at first?
- What percentage of the children at the safari park were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
7 u |
10 u |
(+ 62) |
+ 1.05 u (+ 42) |
+ 2.6 u (+ 104) |
3 u + 62 |
8.05 u |
12.6 u |
Number of boys that entered the safari park
= 15% x 7 u
=
15100 x 7 u
= 1.05 u
1.05 u = 42
1 u = 42 ÷ 1.05 = 40
Number of girls at first
= 3 u
= 3 x 40
= 120
(b)
Increase in the number of children
= 26% x 10 u
=
26100 x 10 u
= 2.6 u
Total number of children at the safari park in the end
= 10 u + 2.6 u
= 12.6 u
= 12.6 x 40
= 504
Increase in the number of girls
= 104 - 42
= 62
Total number of girls in the end
= 3 u + 62
= 3 x 40 + 62
= 182
Percentage of children who were girls
=
182504 x 100
= 36
19%
Answer(s): (a) 120; (b) 36
19%