At first, the ratio of the number of boys to the number of girls at a tourist attraction was 2 : 5. When 48 girls and some boys entered the tourist attraction, the number of girls increased by 15% and the total number of children at the tourist attraction increased by 25%.

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

(a)

Boys	Girls	Total
2 u	5 u	7 u
(+ 64)	+ 0.75 u (+ 48)	+ 1.75 u (+ 112)
2 u + 64	5.75 u	8.75 u

Number of girls that entered the tourist attraction
= 15% x 5 u
= ¹⁵₁₀₀ x 5 u
= 0.75 u

0.75 u = 48

1 u = 48 ÷ 0.75 = 64

Number of boys at first
= 2 u
= 2 x 64
= 128

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

Total number of children at the tourist attraction in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 64
= 560

Increase in the number of boys
= 112 - 48
= 64

Total number of boys in the end
= 2 u + 64
= 2 x 64 + 64
= 192

Percentage of children who were boys
= ¹⁹²₅₆₀ x 100
= 34²₇%

Answer(s): (a) 128; (b) 34²₇%