At first, the ratio of the number of boys to the number of girls at a tourist attraction was 3 : 5. When 44 girls and some boys entered the tourist attraction, the number of girls increased by 11% and the total number of children at the tourist attraction increased by 25%.
- How many boys were there at first?
- What percentage of the children at the tourist attraction were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
5 u |
8 u |
(+ 116) |
+ 0.55 u (+ 44) |
+ 2 u (+ 160) |
3 u + 116 |
5.55 u |
10 u |
Number of girls that entered the tourist attraction
= 11% x 5 u
=
11100 x 5 u
= 0.55 u
0.55 u = 44
1 u = 44 ÷ 0.55 = 80
Number of boys at first
= 3 u
= 3 x 80
= 240
(b)
Increase in the number of children
= 25% x 8 u
=
25100 x 8 u
= 2 u
Total number of children at the tourist attraction in the end
= 8 u + 2 u
= 10 u
= 10 x 80
= 800
Increase in the number of boys
= 160 - 44
= 116
Total number of boys in the end
= 3 u + 116
= 3 x 80 + 116
= 356
Percentage of children who were boys
=
356800 x 100
= 44
12%
Answer(s): (a) 240; (b) 44
12%