At first, the ratio of the number of girls to the number of boys at a museum was 2 : 5. When 54 boys and some girls entered the museum, the number of boys increased by 15% and the total number of children at the museum increased by 25%.

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

(a)

Girls	Boys	Total
2 u	5 u	7 u
(+ 72)	+ 0.75 u (+ 54)	+ 1.75 u (+ 126)
2 u + 72	5.75 u	8.75 u

Number of boys that entered the museum
= 15% x 5 u
= ¹⁵₁₀₀ x 5 u
= 0.75 u

0.75 u = 54

1 u = 54 ÷ 0.75 = 72

Number of girls at first
= 2 u
= 2 x 72
= 144

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

Total number of children at the museum in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 72
= 630

Increase in the number of girls
= 126 - 54
= 72

Total number of girls in the end
= 2 u + 72
= 2 x 72 + 72
= 216

Percentage of children who were girls
= ²¹⁶₆₃₀ x 100
= 34²₇%

Answer(s): (a) 144; (b) 34²₇%