At first, the ratio of the number of boys to the number of girls at a stadium was 4 : 5. When 60 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 28%.
- 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 |
(+ 192) |
+ 0.6 u (+ 60) |
+ 2.52 u (+ 252) |
4 u + 192 |
5.6 u |
11.52 u |
Number of girls that entered the stadium
= 12% x 5 u
=
12100 x 5 u
= 0.6 u
0.6 u = 60
1 u = 60 ÷ 0.6 = 100
Number of boys at first
= 4 u
= 4 x 100
= 400
(b)
Increase in the number of children
= 28% x 9 u
=
28100 x 9 u
= 2.52 u
Total number of children at the stadium in the end
= 9 u + 2.52 u
= 11.52 u
= 11.52 x 100
= 1152
Increase in the number of boys
= 252 - 60
= 192
Total number of boys in the end
= 4 u + 192
= 4 x 100 + 192
= 592
Percentage of children who were boys
=
5921152 x 100
= 51
718%
Answer(s): (a) 400; (b) 51
718%