At first, the ratio of the number of boys to the number of girls at a theme park was 3 : 7. When 42 girls and some boys entered the theme park, the number of girls increased by 10% and the total number of children at the theme park increased by 25%.
- 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 |
7 u |
10 u |
(+ 108) |
+ 0.7 u (+ 42) |
+ 2.5 u (+ 150) |
3 u + 108 |
7.7 u |
12.5 u |
Number of girls that entered the theme park
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 42
1 u = 42 ÷ 0.7 = 60
Number of boys at first
= 3 u
= 3 x 60
= 180
(b)
Increase in the number of children
= 25% x 10 u
=
25100 x 10 u
= 2.5 u
Total number of children at the theme park in the end
= 10 u + 2.5 u
= 12.5 u
= 12.5 x 60
= 750
Increase in the number of boys
= 150 - 42
= 108
Total number of boys in the end
= 3 u + 108
= 3 x 60 + 108
= 288
Percentage of children who were boys
=
288750 x 100
= 38
25%
Answer(s): (a) 180; (b) 38
25%