At first, the ratio of the number of boys to the number of girls at a stadium was 3 : 5. When 48 girls and some boys entered the stadium, the number of girls increased by 12% and the total number of children at the stadium increased by 20%.
- 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) |
+ 0.6 u (+ 48) |
+ 1.6 u (+ 128) |
3 u + 80 |
5.6 u |
9.6 u |
Number of girls that entered the stadium
= 12% x 5 u
=
12100 x 5 u
= 0.6 u
0.6 u = 48
1 u = 48 ÷ 0.6 = 80
Number of boys at first
= 3 u
= 3 x 80
= 240
(b)
Increase in the number of children
= 20% x 8 u
=
20100 x 8 u
= 1.6 u
Total number of children at the stadium in the end
= 8 u + 1.6 u
= 9.6 u
= 9.6 x 80
= 768
Increase in the number of boys
= 128 - 48
= 80
Total number of boys in the end
= 3 u + 80
= 3 x 80 + 80
= 320
Percentage of children who were boys
=
320768 x 100
= 41
23%
Answer(s): (a) 240; (b) 41
23%