At first, the ratio of the number of boys to the number of girls at a concert hall was 3 : 5. When 45 girls and some boys entered the concert hall, the number of girls increased by 12% and the total number of children at the concert hall increased by 26%.

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

(a)

Boys	Girls	Total
3 u	5 u	8 u
(+ 111)	+ 0.6 u (+ 45)	+ 2.08 u (+ 156)
3 u + 111	5.6 u	10.08 u

Number of girls that entered the concert hall
= 12% x 5 u
= ¹²₁₀₀ x 5 u
= 0.6 u

0.6 u = 45

1 u = 45 ÷ 0.6 = 75

Number of boys at first
= 3 u
= 3 x 75
= 225

(b)
Increase in the number of children
= 26% x 8 u
= ²⁶₁₀₀ x 8 u
= 2.08 u

Total number of children at the concert hall in the end
= 8 u + 2.08 u
= 10.08 u
= 10.08 x 75
= 756

Increase in the number of boys
= 156 - 45
= 111

Total number of boys in the end
= 3 u + 111
= 3 x 75 + 111
= 336

Percentage of children who were boys
= ³³⁶₇₅₆ x 100
= 44⁴₉%

Answer(s): (a) 225; (b) 44⁴₉%