At first, the ratio of the number of boys to the number of girls at a stadium was 2 : 5. When 51 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 |
2 u |
5 u |
7 u |
(+ 68) |
+ 0.75 u (+ 51) |
+ 1.75 u (+ 119) |
2 u + 68 |
5.75 u |
8.75 u |
Number of girls that entered the stadium
= 15% x 5 u
=
15100 x 5 u
= 0.75 u
0.75 u = 51
1 u = 51 ÷ 0.75 = 68
Number of boys at first
= 2 u
= 2 x 68
= 136
(b)
Increase in the number of children
= 25% x 7 u
=
25100 x 7 u
= 1.75 u
Total number of children at the stadium in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 68
= 595
Increase in the number of boys
= 119 - 51
= 68
Total number of boys in the end
= 2 u + 68
= 2 x 68 + 68
= 204
Percentage of children who were boys
=
204595 x 100
= 34
27%
Answer(s): (a) 136; (b) 34
27%