At first, the ratio of the number of boys to the number of girls at a tourist attraction was 3 : 5. When 50 girls and some boys entered the tourist attraction, the number of girls increased by 10% and the total number of children at the tourist attraction increased by 32%.

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
3 u	5 u	8 u
(+ 206)	+ 0.5 u (+ 50)	+ 2.56 u (+ 256)
3 u + 206	5.5 u	10.56 u

Number of girls that entered the tourist attraction
= 10% x 5 u
= ¹⁰₁₀₀ x 5 u
= 0.5 u

0.5 u = 50

1 u = 50 ÷ 0.5 = 100

Number of boys at first
= 3 u
= 3 x 100
= 300

(b)
Increase in the number of children
= 32% x 8 u
= ³²₁₀₀ x 8 u
= 2.56 u

Total number of children at the tourist attraction in the end
= 8 u + 2.56 u
= 10.56 u
= 10.56 x 100
= 1056

Increase in the number of boys
= 256 - 50
= 206

Total number of boys in the end
= 3 u + 206
= 3 x 100 + 206
= 506

Percentage of children who were boys
= ⁵⁰⁶₁₀₅₆ x 100
= 47¹¹₁₂%

Answer(s): (a) 300; (b) 47¹¹₁₂%