At first, the ratio of the number of girls to the number of boys at a museum was 3 : 7. When 42 boys and some girls entered the museum, the number of boys increased by 10% and the total number of children at the museum increased by 33%.
- How many girls were there at first?
- What percentage of the children at the museum were girls in the end? Express your answer as a mixed number.
(a)
Girls |
Boys |
Total |
3 u |
7 u |
10 u |
(+ 156) |
+ 0.7 u (+ 42) |
+ 3.3 u (+ 198) |
3 u + 156 |
7.7 u |
13.3 u |
Number of boys that entered the museum
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 42
1 u = 42 ÷ 0.7 = 60
Number of girls at first
= 3 u
= 3 x 60
= 180
(b)
Increase in the number of children
= 33% x 10 u
=
33100 x 10 u
= 3.3 u
Total number of children at the museum in the end
= 10 u + 3.3 u
= 13.3 u
= 13.3 x 60
= 798
Increase in the number of girls
= 198 - 42
= 156
Total number of girls in the end
= 3 u + 156
= 3 x 60 + 156
= 336
Percentage of children who were girls
=
336798 x 100
= 42
219%
Answer(s): (a) 180; (b) 42
219%