At first, the ratio of the number of boys to the number of girls at a theme park was 3 : 5. When 52 girls and some boys entered the theme park, the number of girls increased by 16% and the total number of children at the theme park increased by 30%.
- How many boys were there at first?
- What percentage of the children at the theme park were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
5 u |
8 u |
(+ 104) |
+ 0.8 u (+ 52) |
+ 2.4 u (+ 156) |
3 u + 104 |
5.8 u |
10.4 u |
Number of girls that entered the theme park
= 16% x 5 u
=
16100 x 5 u
= 0.8 u
0.8 u = 52
1 u = 52 ÷ 0.8 = 65
Number of boys at first
= 3 u
= 3 x 65
= 195
(b)
Increase in the number of children
= 30% x 8 u
=
30100 x 8 u
= 2.4 u
Total number of children at the theme park in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 65
= 676
Increase in the number of boys
= 156 - 52
= 104
Total number of boys in the end
= 3 u + 104
= 3 x 65 + 104
= 299
Percentage of children who were boys
=
299676 x 100
= 44
313%
Answer(s): (a) 195; (b) 44
313%