At first, the ratio of the number of boys to the number of girls at a safari park was 4 : 5. When 46 girls and some boys entered the safari park, the number of girls increased by 10% and the total number of children at the safari park increased by 25%.

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

(a)

Boys	Girls	Total
4 u	5 u	9 u
(+ 161)	+ 0.5 u (+ 46)	+ 2.25 u (+ 207)
4 u + 161	5.5 u	11.25 u

Number of girls that entered the safari park
= 10% x 5 u
= ¹⁰₁₀₀ x 5 u
= 0.5 u

0.5 u = 46

1 u = 46 ÷ 0.5 = 92

Number of boys at first
= 4 u
= 4 x 92
= 368

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

Total number of children at the safari park in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 92
= 1035

Increase in the number of boys
= 207 - 46
= 161

Total number of boys in the end
= 4 u + 161
= 4 x 92 + 161
= 529

Percentage of children who were boys
= ⁵²⁹₁₀₃₅ x 100
= 51¹₉%

Answer(s): (a) 368; (b) 51¹₉%