At first, the ratio of the number of girls to the number of boys at a museum was 3 : 7. When 56 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 21%.
- 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 |
(+ 112) |
+ 0.7 u (+ 56) |
+ 2.1 u (+ 168) |
3 u + 112 |
7.7 u |
12.1 u |
Number of boys that entered the museum
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 56
1 u = 56 ÷ 0.7 = 80
Number of girls at first
= 3 u
= 3 x 80
= 240
(b)
Increase in the number of children
= 21% x 10 u
=
21100 x 10 u
= 2.1 u
Total number of children at the museum in the end
= 10 u + 2.1 u
= 12.1 u
= 12.1 x 80
= 968
Increase in the number of girls
= 168 - 56
= 112
Total number of girls in the end
= 3 u + 112
= 3 x 80 + 112
= 352
Percentage of children who were girls
=
352968 x 100
= 36
411%
Answer(s): (a) 240; (b) 36
411%