At first, the ratio of the number of boys to the number of girls at a park was 2 : 5. When 56 girls and some boys entered the park, the number of girls increased by 14% and the total number of children at the park increased by 20%.
- How many boys were there at first?
- What percentage of the children at the park were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
2 u |
5 u |
7 u |
(+ 56) |
+ 0.7 u (+ 56) |
+ 1.4 u (+ 112) |
2 u + 56 |
5.7 u |
8.4 u |
Number of girls that entered the park
= 14% x 5 u
=
14100 x 5 u
= 0.7 u
0.7 u = 56
1 u = 56 ÷ 0.7 = 80
Number of boys at first
= 2 u
= 2 x 80
= 160
(b)
Increase in the number of children
= 20% x 7 u
=
20100 x 7 u
= 1.4 u
Total number of children at the park in the end
= 7 u + 1.4 u
= 8.4 u
= 8.4 x 80
= 672
Increase in the number of boys
= 112 - 56
= 56
Total number of boys in the end
= 2 u + 56
= 2 x 80 + 56
= 216
Percentage of children who were boys
=
216672 x 100
= 32
17%
Answer(s): (a) 160; (b) 32
17%