At first, the ratio of the number of boys to the number of girls at a zoo was 4 : 7. When 49 girls and some boys entered the zoo, the number of girls increased by 10% and the total number of children at the zoo increased by 20%.
- 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 |
4 u |
7 u |
11 u |
(+ 105) |
+ 0.7 u (+ 49) |
+ 2.2 u (+ 154) |
4 u + 105 |
7.7 u |
13.2 u |
Number of girls that entered the zoo
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 49
1 u = 49 ÷ 0.7 = 70
Number of boys at first
= 4 u
= 4 x 70
= 280
(b)
Increase in the number of children
= 20% x 11 u
=
20100 x 11 u
= 2.2 u
Total number of children at the zoo in the end
= 11 u + 2.2 u
= 13.2 u
= 13.2 x 70
= 924
Increase in the number of boys
= 154 - 49
= 105
Total number of boys in the end
= 4 u + 105
= 4 x 70 + 105
= 385
Percentage of children who were boys
=
385924 x 100
= 41
23%
Answer(s): (a) 280; (b) 41
23%