At first, the ratio of the number of boys to the number of girls at a concert hall was 2 : 5. When 56 girls and some boys entered the concert hall, the number of girls increased by 10% 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 |
2 u |
5 u |
7 u |
(+ 140) |
+ 0.5 u (+ 56) |
+ 1.75 u (+ 196) |
2 u + 140 |
5.5 u |
8.75 u |
Number of girls that entered the concert hall
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
0.5 u = 56
1 u = 56 ÷ 0.5 = 112
Number of boys at first
= 2 u
= 2 x 112
= 224
(b)
Increase in the number of children
= 25% x 7 u
=
25100 x 7 u
= 1.75 u
Total number of children at the concert hall in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 112
= 980
Increase in the number of boys
= 196 - 56
= 140
Total number of boys in the end
= 2 u + 140
= 2 x 112 + 140
= 364
Percentage of children who were boys
=
364980 x 100
= 37
17%
Answer(s): (a) 224; (b) 37
17%