At first, the ratio of the number of boys to the number of girls at a concert hall was 3 : 5. When 55 girls and some boys entered the concert hall, the number of girls increased by 11% 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 |
3 u |
5 u |
8 u |
(+ 145) |
+ 0.55 u (+ 55) |
+ 2 u (+ 200) |
3 u + 145 |
5.55 u |
10 u |
Number of girls that entered the concert hall
= 11% x 5 u
=
11100 x 5 u
= 0.55 u
0.55 u = 55
1 u = 55 ÷ 0.55 = 100
Number of boys at first
= 3 u
= 3 x 100
= 300
(b)
Increase in the number of children
= 25% x 8 u
=
25100 x 8 u
= 2 u
Total number of children at the concert hall in the end
= 8 u + 2 u
= 10 u
= 10 x 100
= 1000
Increase in the number of boys
= 200 - 55
= 145
Total number of boys in the end
= 3 u + 145
= 3 x 100 + 145
= 445
Percentage of children who were boys
=
4451000 x 100
= 44
12%
Answer(s): (a) 300; (b) 44
12%