At first, the ratio of the number of girls to the number of boys at a park was 4 : 5. When 44 boys and some girls entered the park, the number of boys increased by 11% and the total number of children at the park increased by 25%.

1. How many girls were there at first?
2. What percentage of the children at the park were girls in the end? Express your answer as a mixed number.

(a)

Girls	Boys	Total
4 u	5 u	9 u
(+ 136)	+ 0.55 u (+ 44)	+ 2.25 u (+ 180)
4 u + 136	5.55 u	11.25 u

Number of boys that entered the park
= 11% x 5 u
= ¹¹₁₀₀ x 5 u
= 0.55 u

0.55 u = 44

1 u = 44 ÷ 0.55 = 80

Number of girls at first
= 4 u
= 4 x 80
= 320

(b)
Increase in the number of children
= 25% x 9 u
= ²⁵₁₀₀ x 9 u
= 2.25 u

Total number of children at the park in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 80
= 900

Increase in the number of girls
= 180 - 44
= 136

Total number of girls in the end
= 4 u + 136
= 4 x 80 + 136
= 456

Percentage of children who were girls
= ⁴⁵⁶₉₀₀ x 100
= 50²₃%

Answer(s): (a) 320; (b) 50²₃%