At first, the ratio of the number of girls to the number of boys at a bird park was 2 : 7. When 49 boys and some girls entered the bird park, the number of boys increased by 14% and the total number of children at the bird park increased by 20%.

1. How many girls were there at first?
2. 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	7 u	9 u
(+ 41)	+ 0.98 u (+ 49)	+ 1.8 u (+ 90)
2 u + 41	7.98 u	10.8 u

Number of boys that entered the bird park
= 14% x 7 u
= ¹⁴₁₀₀ x 7 u
= 0.98 u

0.98 u = 49

1 u = 49 ÷ 0.98 = 50

Number of girls at first
= 2 u
= 2 x 50
= 100

(b)
Increase in the number of children
= 20% x 9 u
= ²⁰₁₀₀ x 9 u
= 1.8 u

Total number of children at the bird park in the end
= 9 u + 1.8 u
= 10.8 u
= 10.8 x 50
= 540

Increase in the number of girls
= 90 - 49
= 41

Total number of girls in the end
= 2 u + 41
= 2 x 50 + 41
= 141

Percentage of children who were girls
= ¹⁴¹₅₄₀ x 100
= 26¹₉%

Answer(s): (a) 100; (b) 26¹₉%