At first, the ratio of the number of boys to the number of girls at a concert hall was 4 : 5. When 48 girls and some boys entered the concert hall, the number of girls increased by 12% and the total number of children at the concert hall increased by 25%.
- How many boys were there at first?
- What percentage of the children at the concert hall were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
4 u |
5 u |
9 u |
(+ 132) |
+ 0.6 u (+ 48) |
+ 2.25 u (+ 180) |
4 u + 132 |
5.6 u |
11.25 u |
Number of girls that entered the concert hall
= 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
= 4 u
= 4 x 80
= 320
(b)
Increase in the number of children
= 25% x 9 u
=
25100 x 9 u
= 2.25 u
Total number of children at the concert hall in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 80
= 900
Increase in the number of boys
= 180 - 48
= 132
Total number of boys in the end
= 4 u + 132
= 4 x 80 + 132
= 452
Percentage of children who were boys
=
452900 x 100
= 50
29%
Answer(s): (a) 320; (b) 50
29%