At first, the ratio of the number of girls to the number of boys at a tourist attraction was 4 : 5. When 48 boys and some girls entered the tourist attraction, the number of boys increased by 10% and the total number of children at the tourist attraction increased by 25%.
- 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 |
4 u |
5 u |
9 u |
(+ 168) |
+ 0.5 u (+ 48) |
+ 2.25 u (+ 216) |
4 u + 168 |
5.5 u |
11.25 u |
Number of boys that entered the tourist attraction
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
0.5 u = 48
1 u = 48 ÷ 0.5 = 96
Number of girls at first
= 4 u
= 4 x 96
= 384
(b)
Increase in the number of children
= 25% x 9 u
=
25100 x 9 u
= 2.25 u
Total number of children at the tourist attraction in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 96
= 1080
Increase in the number of girls
= 216 - 48
= 168
Total number of girls in the end
= 4 u + 168
= 4 x 96 + 168
= 552
Percentage of children who were girls
=
5521080 x 100
= 51
19%
Answer(s): (a) 384; (b) 51
19%