At first, the ratio of the number of girls to the number of boys at a stadium was 3 : 5. When 57 boys and some girls entered the stadium, the number of boys increased by 15% and the total number of children at the stadium increased by 25%.
- How many girls were there at first?
- What percentage of the children at the stadium were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
5 u |
8 u |
(+ 95) |
+ 0.75 u (+ 57) |
+ 2 u (+ 152) |
3 u + 95 |
5.75 u |
10 u |
Number of boys that entered the stadium
= 15% x 5 u
=
15100 x 5 u
= 0.75 u
0.75 u = 57
1 u = 57 ÷ 0.75 = 76
Number of girls at first
= 3 u
= 3 x 76
= 228
(b)
Increase in the number of children
= 25% x 8 u
=
25100 x 8 u
= 2 u
Total number of children at the stadium in the end
= 8 u + 2 u
= 10 u
= 10 x 76
= 760
Increase in the number of girls
= 152 - 57
= 95
Total number of girls in the end
= 3 u + 95
= 3 x 76 + 95
= 323
Percentage of children who were girls
=
323760 x 100
= 42
12%
Answer(s): (a) 228; (b) 42
12%