At first, the ratio of the number of boys to the number of girls at a stadium was 3 : 5. When 45 girls and some boys entered the stadium, the number of girls increased by 15% 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 |
3 u |
5 u |
8 u |
(+ 75) |
+ 0.75 u (+ 45) |
+ 2 u (+ 120) |
3 u + 75 |
5.75 u |
10 u |
Number of girls that entered the stadium
= 15% x 5 u
=
15100 x 5 u
= 0.75 u
0.75 u = 45
1 u = 45 ÷ 0.75 = 60
Number of boys at first
= 3 u
= 3 x 60
= 180
(b)
Increase in the number of children
= 25% x 8 u
=
25100 x 8 u
= 2 u
Total number of children at the stadium in the end
= 8 u + 2 u
= 10 u
= 10 x 60
= 600
Increase in the number of boys
= 120 - 45
= 75
Total number of boys in the end
= 3 u + 75
= 3 x 60 + 75
= 255
Percentage of children who were boys
=
255600 x 100
= 42
12%
Answer(s): (a) 180; (b) 42
12%