At first, the ratio of the number of boys to the number of girls at a park was 3 : 5. When 51 girls and some boys entered the park, the number of girls increased by 12% and the total number of children at the park increased by 30%.

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

(a)

Boys	Girls	Total
3 u	5 u	8 u
(+ 153)	+ 0.6 u (+ 51)	+ 2.4 u (+ 204)
3 u + 153	5.6 u	10.4 u

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

0.6 u = 51

1 u = 51 ÷ 0.6 = 85

Number of boys at first
= 3 u
= 3 x 85
= 255

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

Total number of children at the park in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 85
= 884

Increase in the number of boys
= 204 - 51
= 153

Total number of boys in the end
= 3 u + 153
= 3 x 85 + 153
= 408

Percentage of children who were boys
= ⁴⁰⁸₈₈₄ x 100
= 46²₁₃%

Answer(s): (a) 255; (b) 46²₁₃%