At first, the ratio of the number of boys to the number of girls at a zoo was 3 : 7. When 42 girls and some boys entered the zoo, the number of girls increased by 12% and the total number of children at the zoo increased by 33%.
- 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 |
7 u |
10 u |
(+ 123) |
+ 0.84 u (+ 42) |
+ 3.3 u (+ 165) |
3 u + 123 |
7.84 u |
13.3 u |
Number of girls that entered the zoo
= 12% x 7 u
=
12100 x 7 u
= 0.84 u
0.84 u = 42
1 u = 42 ÷ 0.84 = 50
Number of boys at first
= 3 u
= 3 x 50
= 150
(b)
Increase in the number of children
= 33% x 10 u
=
33100 x 10 u
= 3.3 u
Total number of children at the zoo in the end
= 10 u + 3.3 u
= 13.3 u
= 13.3 x 50
= 665
Increase in the number of boys
= 165 - 42
= 123
Total number of boys in the end
= 3 u + 123
= 3 x 50 + 123
= 273
Percentage of children who were boys
=
273665 x 100
= 41
119%
Answer(s): (a) 150; (b) 41
119%