At first, the ratio of the number of girls to the number of boys at a theme park was 3 : 5. When 54 boys and some girls entered the theme park, the number of boys increased by 12% and the total number of children at the theme park increased by 30%.

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
3 u	5 u	8 u
(+ 162)	+ 0.6 u (+ 54)	+ 2.4 u (+ 216)
3 u + 162	5.6 u	10.4 u

Number of boys that entered the theme park
= 12% x 5 u
= ¹²₁₀₀ x 5 u
= 0.6 u

0.6 u = 54

1 u = 54 ÷ 0.6 = 90

Number of girls at first
= 3 u
= 3 x 90
= 270

(b)
Increase in the number of children
= 30% x 8 u
= ³⁰₁₀₀ x 8 u
= 2.4 u

Total number of children at the theme park in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 90
= 936

Increase in the number of girls
= 216 - 54
= 162

Total number of girls in the end
= 3 u + 162
= 3 x 90 + 162
= 432

Percentage of children who were girls
= ⁴³²₉₃₆ x 100
= 46²₁₃%

Answer(s): (a) 270; (b) 46²₁₃%