At first, the ratio of the number of girls to the number of boys at a park was 2 : 5. When 57 boys and some girls entered the park, the number of boys increased by 15% and the total number of children at the park increased by 25%.
- 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 |
2 u |
5 u |
7 u |
(+ 76) |
+ 0.75 u (+ 57) |
+ 1.75 u (+ 133) |
2 u + 76 |
5.75 u |
8.75 u |
Number of boys that entered the park
= 15% x 5 u
=
15100 x 5 u
= 0.75 u
0.75 u = 57
1 u = 57 ÷ 0.75 = 76
Number of girls at first
= 2 u
= 2 x 76
= 152
(b)
Increase in the number of children
= 25% x 7 u
=
25100 x 7 u
= 1.75 u
Total number of children at the park in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 76
= 665
Increase in the number of girls
= 133 - 57
= 76
Total number of girls in the end
= 2 u + 76
= 2 x 76 + 76
= 228
Percentage of children who were girls
=
228665 x 100
= 34
27%
Answer(s): (a) 152; (b) 34
27%