At first, the ratio of the number of boys to the number of girls at a bird park was 3 : 7. When 42 girls and some boys entered the bird park, the number of girls increased by 10% and the total number of children at the bird park increased by 26%.
- How many boys were there at first?
- What percentage of the children at the bird park were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
7 u |
10 u |
(+ 114) |
+ 0.7 u (+ 42) |
+ 2.6 u (+ 156) |
3 u + 114 |
7.7 u |
12.6 u |
Number of girls that entered the bird park
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 42
1 u = 42 ÷ 0.7 = 60
Number of boys at first
= 3 u
= 3 x 60
= 180
(b)
Increase in the number of children
= 26% x 10 u
=
26100 x 10 u
= 2.6 u
Total number of children at the bird park in the end
= 10 u + 2.6 u
= 12.6 u
= 12.6 x 60
= 756
Increase in the number of boys
= 156 - 42
= 114
Total number of boys in the end
= 3 u + 114
= 3 x 60 + 114
= 294
Percentage of children who were boys
=
294756 x 100
= 38
89%
Answer(s): (a) 180; (b) 38
89%