At first, the ratio of the number of girls to the number of boys at a tourist attraction was 2 : 5. When 42 boys and some girls entered the tourist attraction, the number of boys increased by 12% and the total number of children at the tourist attraction increased by 30%.
- How many girls were there at first?
- What percentage of the children at the tourist attraction were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
2 u |
5 u |
7 u |
(+ 105) |
+ 0.6 u (+ 42) |
+ 2.1 u (+ 147) |
2 u + 105 |
5.6 u |
9.1 u |
Number of boys that entered the tourist attraction
= 12% x 5 u
=
12100 x 5 u
= 0.6 u
0.6 u = 42
1 u = 42 ÷ 0.6 = 70
Number of girls at first
= 2 u
= 2 x 70
= 140
(b)
Increase in the number of children
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Total number of children at the tourist attraction in the end
= 7 u + 2.1 u
= 9.1 u
= 9.1 x 70
= 637
Increase in the number of girls
= 147 - 42
= 105
Total number of girls in the end
= 2 u + 105
= 2 x 70 + 105
= 245
Percentage of children who were girls
=
245637 x 100
= 38
613%
Answer(s): (a) 140; (b) 38
613%