At first, the ratio of the number of girls to the number of boys at a theme park was 4 : 5. When 42 boys and some girls entered the theme park, the number of boys increased by 14% and the total number of children at the theme park increased by 25%.

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

(a)

Girls	Boys	Total
4 u	5 u	9 u
(+ 93)	+ 0.7 u (+ 42)	+ 2.25 u (+ 135)
4 u + 93	5.7 u	11.25 u

Number of boys that entered the theme park
= 14% x 5 u
= ¹⁴₁₀₀ x 5 u
= 0.7 u

0.7 u = 42

1 u = 42 ÷ 0.7 = 60

Number of girls at first
= 4 u
= 4 x 60
= 240

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

Total number of children at the theme park in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 60
= 675

Increase in the number of girls
= 135 - 42
= 93

Total number of girls in the end
= 4 u + 93
= 4 x 60 + 93
= 333

Percentage of children who were girls
= ³³³₆₇₅ x 100
= 49¹₃%

Answer(s): (a) 240; (b) 49¹₃%