At first, the ratio of the number of boys to the number of girls at a stadium was 3 : 5. When 40 girls and some boys entered the stadium, the number of girls increased by 16% and the total number of children at the stadium increased by 30%.
- How many boys were there at first?
- What percentage of the children at the stadium were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
5 u |
8 u |
(+ 80) |
+ 0.8 u (+ 40) |
+ 2.4 u (+ 120) |
3 u + 80 |
5.8 u |
10.4 u |
Number of girls that entered the stadium
= 16% x 5 u
=
16100 x 5 u
= 0.8 u
0.8 u = 40
1 u = 40 ÷ 0.8 = 50
Number of boys at first
= 3 u
= 3 x 50
= 150
(b)
Increase in the number of children
= 30% x 8 u
=
30100 x 8 u
= 2.4 u
Total number of children at the stadium in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 50
= 520
Increase in the number of boys
= 120 - 40
= 80
Total number of boys in the end
= 3 u + 80
= 3 x 50 + 80
= 230
Percentage of children who were boys
=
230520 x 100
= 44
313%
Answer(s): (a) 150; (b) 44
313%