At first, the ratio of the number of boys to the number of girls at a park was 3 : 5. When 45 girls and some boys entered the park, the number of girls increased by 12% and the total number of children at the park increased by 28%.
- How many boys were there at first?
- What percentage of the children at the park were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
5 u |
8 u |
(+ 123) |
+ 0.6 u (+ 45) |
+ 2.24 u (+ 168) |
3 u + 123 |
5.6 u |
10.24 u |
Number of girls that entered the park
= 12% x 5 u
=
12100 x 5 u
= 0.6 u
0.6 u = 45
1 u = 45 ÷ 0.6 = 75
Number of boys at first
= 3 u
= 3 x 75
= 225
(b)
Increase in the number of children
= 28% x 8 u
=
28100 x 8 u
= 2.24 u
Total number of children at the park in the end
= 8 u + 2.24 u
= 10.24 u
= 10.24 x 75
= 768
Increase in the number of boys
= 168 - 45
= 123
Total number of boys in the end
= 3 u + 123
= 3 x 75 + 123
= 348
Percentage of children who were boys
=
348768 x 100
= 45
516%
Answer(s): (a) 225; (b) 45
516%