At first, the ratio of the number of boys to the number of girls at a zoo was 3 : 7. When 42 girls and some boys entered the zoo, the number of girls increased by 15% and the total number of children at the zoo increased by 20%.

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

(a)

Boys	Girls	Total
3 u	7 u	10 u
(+ 38)	+ 1.05 u (+ 42)	+ 2 u (+ 80)
3 u + 38	8.05 u	12 u

Number of girls that entered the zoo
= 15% x 7 u
= ¹⁵₁₀₀ x 7 u
= 1.05 u

1.05 u = 42

1 u = 42 ÷ 1.05 = 40

Number of boys at first
= 3 u
= 3 x 40
= 120

(b)
Increase in the number of children
= 20% x 10 u
= ²⁰₁₀₀ x 10 u
= 2 u

Total number of children at the zoo in the end
= 10 u + 2 u
= 12 u
= 12 x 40
= 480

Increase in the number of boys
= 80 - 42
= 38

Total number of boys in the end
= 3 u + 38
= 3 x 40 + 38
= 158

Percentage of children who were boys
= ¹⁵⁸₄₈₀ x 100
= 32¹¹₁₂%

Answer(s): (a) 120; (b) 32¹¹₁₂%