At first, the ratio of the number of boys to the number of girls at a zoo was 3 : 5. When 51 girls and some boys entered the zoo, the number of girls increased by 17% and the total number of children at the zoo increased by 30%.
- How many boys were there at first?
- What percentage of the children at the zoo were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
5 u |
8 u |
(+ 93) |
+ 0.85 u (+ 51) |
+ 2.4 u (+ 144) |
3 u + 93 |
5.85 u |
10.4 u |
Number of girls 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 boys at first
= 3 u
= 3 x 60
= 180
(b)
Increase in the number of children
= 30% x 8 u
=
30100 x 8 u
= 2.4 u
Total number of children at the zoo in the end
= 8 u + 2.4 u
= 10.4 u
= 10.4 x 60
= 624
Increase in the number of boys
= 144 - 51
= 93
Total number of boys in the end
= 3 u + 93
= 3 x 60 + 93
= 273
Percentage of children who were boys
=
273624 x 100
= 43
34%
Answer(s): (a) 180; (b) 43
34%