At first, the ratio of the number of boys to the number of girls at a zoo was 2 : 5. When 40 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 25%.
- 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 |
2 u |
5 u |
7 u |
(+ 100) |
+ 0.5 u (+ 40) |
+ 1.75 u (+ 140) |
2 u + 100 |
5.5 u |
8.75 u |
Number of girls that entered the zoo
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
0.5 u = 40
1 u = 40 ÷ 0.5 = 80
Number of boys at first
= 2 u
= 2 x 80
= 160
(b)
Increase in the number of children
= 25% x 7 u
=
25100 x 7 u
= 1.75 u
Total number of children at the zoo in the end
= 7 u + 1.75 u
= 8.75 u
= 8.75 x 80
= 700
Increase in the number of boys
= 140 - 40
= 100
Total number of boys in the end
= 2 u + 100
= 2 x 80 + 100
= 260
Percentage of children who were boys
=
260700 x 100
= 37
17%
Answer(s): (a) 160; (b) 37
17%