At first, the ratio of the number of boys to the number of girls at a tourist attraction was 4 : 5. When 44 girls and some boys entered the tourist attraction, the number of girls increased by 10% 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 |
4 u |
5 u |
9 u |
(+ 154) |
+ 0.5 u (+ 44) |
+ 2.25 u (+ 198) |
4 u + 154 |
5.5 u |
11.25 u |
Number of girls that entered the tourist attraction
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
0.5 u = 44
1 u = 44 ÷ 0.5 = 88
Number of boys at first
= 4 u
= 4 x 88
= 352
(b)
Increase in the number of children
= 25% x 9 u
=
25100 x 9 u
= 2.25 u
Total number of children at the tourist attraction in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 88
= 990
Increase in the number of boys
= 198 - 44
= 154
Total number of boys in the end
= 4 u + 154
= 4 x 88 + 154
= 506
Percentage of children who were boys
=
506990 x 100
= 51
19%
Answer(s): (a) 352; (b) 51
19%