At first, the ratio of the number of boys to the number of girls at a theme park was 3 : 7. When 49 girls and some boys entered the theme park, the number of girls increased by 10% and the total number of children at the theme park increased by 30%.
- How many boys were there at first?
- What percentage of the children at the theme park were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
3 u |
7 u |
10 u |
(+ 161) |
+ 0.7 u (+ 49) |
+ 3 u (+ 210) |
3 u + 161 |
7.7 u |
13 u |
Number of girls that entered the theme park
= 10% x 7 u
=
10100 x 7 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
= 30% x 10 u
=
30100 x 10 u
= 3 u
Total number of children at the theme park in the end
= 10 u + 3 u
= 13 u
= 13 x 70
= 910
Increase in the number of boys
= 210 - 49
= 161
Total number of boys in the end
= 3 u + 161
= 3 x 70 + 161
= 371
Percentage of children who were boys
=
371910 x 100
= 40
1013%
Answer(s): (a) 210; (b) 40
1013%