At first, the ratio of the number of boys to the number of girls at a theme park was 2 : 5. When 52 girls and some boys entered the theme park, the number of girls increased by 13% and the total number of children at the theme park increased by 25%.

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

(a)

Boys	Girls	Total
2 u	5 u	7 u
(+ 88)	+ 0.65 u (+ 52)	+ 1.75 u (+ 140)
2 u + 88	5.65 u	8.75 u

Number of girls that entered the theme park
= 13% x 5 u
= ¹³₁₀₀ x 5 u
= 0.65 u

0.65 u = 52

1 u = 52 ÷ 0.65 = 80

Number of boys at first
= 2 u
= 2 x 80
= 160

(b)
Increase in the number of children
= 25% x 7 u
= ²⁵₁₀₀ x 7 u
= 1.75 u

Total number of children at the theme park in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 80
= 700

Increase in the number of boys
= 140 - 52
= 88

Total number of boys in the end
= 2 u + 88
= 2 x 80 + 88
= 248

Percentage of children who were boys
= ²⁴⁸₇₀₀ x 100
= 35³₇%

Answer(s): (a) 160; (b) 35³₇%