At first, the ratio of the number of girls to the number of boys at a bird park was 2 : 5. When 51 boys and some girls entered the bird park, the number of boys increased by 17% and the total number of children at the bird park increased by 25%.
- How many girls were there at first?
- What percentage of the children at the bird park were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
2 u |
5 u |
7 u |
(+ 54) |
+ 0.85 u (+ 51) |
+ 1.75 u (+ 105) |
2 u + 54 |
5.85 u |
8.75 u |
Number of boys that entered the bird park
= 17% x 5 u
=
17100 x 5 u
= 0.85 u
0.85 u = 51
1 u = 51 ÷ 0.85 = 60
Number of girls at first
= 2 u
= 2 x 60
= 120
(b)
Increase in the number of children
= 25% x 7 u
=
25100 x 7 u
= 1.75 u
Total number of children at the bird park in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 60
= 525
Increase in the number of girls
= 105 - 51
= 54
Total number of girls in the end
= 2 u + 54
= 2 x 60 + 54
= 174
Percentage of children who were girls
=
174525 x 100
= 33
17%
Answer(s): (a) 120; (b) 33
17%