At first, the ratio of the number of boys to the number of girls at a safari park was 3 : 5. When 49 girls and some boys entered the safari park, the number of girls increased by 14% and the total number of children at the safari park increased by 35%.
- How many boys were there at first?
- What percentage of the children at the safari park were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
5 u |
8 u |
(+ 147) |
+ 0.7 u (+ 49) |
+ 2.8 u (+ 196) |
3 u + 147 |
5.7 u |
10.8 u |
Number of girls that entered the safari park
= 14% x 5 u
=
14100 x 5 u
= 0.7 u
0.7 u = 49
1 u = 49 ÷ 0.7 = 70
Number of boys at first
= 3 u
= 3 x 70
= 210
(b)
Increase in the number of children
= 35% x 8 u
=
35100 x 8 u
= 2.8 u
Total number of children at the safari park in the end
= 8 u + 2.8 u
= 10.8 u
= 10.8 x 70
= 756
Increase in the number of boys
= 196 - 49
= 147
Total number of boys in the end
= 3 u + 147
= 3 x 70 + 147
= 357
Percentage of children who were boys
=
357756 x 100
= 47
29%
Answer(s): (a) 210; (b) 47
29%