At first, the ratio of the number of girls to the number of boys at a zoo was 2 : 5. When 51 boys and some girls entered the zoo, the number of boys increased by 17% and the total number of children at the zoo increased by 30%.
- How many girls were there at first?
- What percentage of the children at the zoo were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
2 u |
5 u |
7 u |
(+ 75) |
+ 0.85 u (+ 51) |
+ 2.1 u (+ 126) |
2 u + 75 |
5.85 u |
9.1 u |
Number of boys that entered the zoo
= 17% x 5 u
=
17100 x 5 u
= 0.85 u
0.85 u = 51
1 u = 51 ÷ 0.85 = 60
Number of girls at first
= 2 u
= 2 x 60
= 120
(b)
Increase in the number of children
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Total number of children at the zoo in the end
= 7 u + 2.1 u
= 9.1 u
= 9.1 x 60
= 546
Increase in the number of girls
= 126 - 51
= 75
Total number of girls in the end
= 2 u + 75
= 2 x 60 + 75
= 195
Percentage of children who were girls
=
195546 x 100
= 35
57%
Answer(s): (a) 120; (b) 35
57%