At first, the ratio of the number of girls to the number of boys at a zoo was 3 : 7. When 42 boys and some girls entered the zoo, the number of boys increased by 12% and the total number of children at the zoo increased by 30%.

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

(a)

Girls	Boys	Total
3 u	7 u	10 u
(+ 108)	+ 0.84 u (+ 42)	+ 3 u (+ 150)
3 u + 108	7.84 u	13 u

Number of boys that entered the zoo
= 12% x 7 u
= ¹²₁₀₀ x 7 u
= 0.84 u

0.84 u = 42

1 u = 42 ÷ 0.84 = 50

Number of girls at first
= 3 u
= 3 x 50
= 150

(b)
Increase in the number of children
= 30% x 10 u
= ³⁰₁₀₀ x 10 u
= 3 u

Total number of children at the zoo in the end
= 10 u + 3 u
= 13 u
= 13 x 50
= 650

Increase in the number of girls
= 150 - 42
= 108

Total number of girls in the end
= 3 u + 108
= 3 x 50 + 108
= 258

Percentage of children who were girls
= ²⁵⁸₆₅₀ x 100
= 39⁹₁₃%

Answer(s): (a) 150; (b) 39⁹₁₃%