At first, the ratio of the number of boys to the number of girls at a concert hall was 2 : 5. When 44 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 20%.
- 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 |
2 u |
5 u |
7 u |
(+ 68) |
+ 0.55 u (+ 44) |
+ 1.4 u (+ 112) |
2 u + 68 |
5.55 u |
8.4 u |
Number of girls that entered the concert hall
= 11% x 5 u
=
11100 x 5 u
= 0.55 u
0.55 u = 44
1 u = 44 ÷ 0.55 = 80
Number of boys at first
= 2 u
= 2 x 80
= 160
(b)
Increase in the number of children
= 20% x 7 u
=
20100 x 7 u
= 1.4 u
Total number of children at the concert hall in the end
= 7 u + 1.4 u
= 8.4 u
= 8.4 x 80
= 672
Increase in the number of boys
= 112 - 44
= 68
Total number of boys in the end
= 2 u + 68
= 2 x 80 + 68
= 228
Percentage of children who were boys
=
228672 x 100
= 33
1314%
Answer(s): (a) 160; (b) 33
1314%