At first, the ratio of the number of girls to the number of boys at a tourist attraction was 3 : 7. When 49 boys and some girls entered the tourist attraction, the number of boys increased by 10% and the total number of children at the tourist attraction increased by 21%.
- How many girls were there at first?
- What percentage of the children at the tourist attraction were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
7 u |
10 u |
(+ 98) |
+ 0.7 u (+ 49) |
+ 2.1 u (+ 147) |
3 u + 98 |
7.7 u |
12.1 u |
Number of boys that entered the tourist attraction
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 49
1 u = 49 ÷ 0.7 = 70
Number of girls at first
= 3 u
= 3 x 70
= 210
(b)
Increase in the number of children
= 21% x 10 u
=
21100 x 10 u
= 2.1 u
Total number of children at the tourist attraction in the end
= 10 u + 2.1 u
= 12.1 u
= 12.1 x 70
= 847
Increase in the number of girls
= 147 - 49
= 98
Total number of girls in the end
= 3 u + 98
= 3 x 70 + 98
= 308
Percentage of children who were girls
=
308847 x 100
= 36
411%
Answer(s): (a) 210; (b) 36
411%