At first, the ratio of the number of boys to the number of girls at a concert hall was 4 : 5. When 56 girls and some boys entered the concert hall, the number of girls increased by 14% 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 |
(+ 124) |
+ 0.7 u (+ 56) |
+ 2.25 u (+ 180) |
4 u + 124 |
5.7 u |
11.25 u |
Number of girls that entered the concert hall
= 14% x 5 u
=
14100 x 5 u
= 0.7 u
0.7 u = 56
1 u = 56 ÷ 0.7 = 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 - 56
= 124
Total number of boys in the end
= 4 u + 124
= 4 x 80 + 124
= 444
Percentage of children who were boys
=
444900 x 100
= 49
13%
Answer(s): (a) 320; (b) 49
13%