At first, the ratio of the number of boys to the number of girls at a stadium was 4 : 5. When 55 girls and some boys entered the stadium, the number of girls increased by 11% and the total number of children at the stadium increased by 25%.
- 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 |
| 4 u |
5 u |
9 u |
| (+ 170) |
+ 0.55 u (+ 55) |
+ 2.25 u (+ 225) |
| 4 u + 170 |
5.55 u |
11.25 u |
Number of girls that entered the stadium
= 11% x 5 u
=
11100 x 5 u
= 0.55 u
0.55 u = 55
1 u = 55 ÷ 0.55 = 100
Number of boys at first
= 4 u
= 4 x 100
= 400
(b)
Increase in the number of children
= 25% x 9 u
=
25100 x 9 u
= 2.25 u
Total number of children at the stadium in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 100
= 1125
Increase in the number of boys
= 225 - 55
= 170
Total number of boys in the end
= 4 u + 170
= 4 x 100 + 170
= 570
Percentage of children who were boys
=
5701125 x 100
= 50
23%
Answer(s): (a) 400; (b) 50
23%
