At first, the ratio of the number of girls to the number of boys at a tourist attraction was 3 : 5. When 51 boys and some girls entered the tourist attraction, the number of boys increased by 17% and the total number of children at the tourist attraction increased by 25%.

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

(a)

Girls	Boys	Total
3 u	5 u	8 u
(+ 69)	+ 0.85 u (+ 51)	+ 2 u (+ 120)
3 u + 69	5.85 u	10 u

Number of boys that entered the tourist attraction
= 17% x 5 u
= ¹⁷₁₀₀ x 5 u
= 0.85 u

0.85 u = 51

1 u = 51 ÷ 0.85 = 60

Number of girls at first
= 3 u
= 3 x 60
= 180

(b)
Increase in the number of children
= 25% x 8 u
= ²⁵₁₀₀ x 8 u
= 2 u

Total number of children at the tourist attraction in the end
= 8 u + 2 u
= 10 u
= 10 x 60
= 600

Increase in the number of girls
= 120 - 51
= 69

Total number of girls in the end
= 3 u + 69
= 3 x 60 + 69
= 249

Percentage of children who were girls
= ²⁴⁹₆₀₀ x 100
= 41¹₂%

Answer(s): (a) 180; (b) 41¹₂%