At first, the ratio of the number of girls to the number of boys at a museum was 2 : 5. When 49 boys and some girls entered the museum, the number of boys increased by 14% and the total number of children at the museum increased by 20%.
- 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 |
2 u |
5 u |
7 u |
(+ 49) |
+ 0.7 u (+ 49) |
+ 1.4 u (+ 98) |
2 u + 49 |
5.7 u |
8.4 u |
Number of boys that entered the museum
= 14% x 5 u
=
14100 x 5 u
= 0.7 u
0.7 u = 49
1 u = 49 ÷ 0.7 = 70
Number of girls at first
= 2 u
= 2 x 70
= 140
(b)
Increase in the number of children
= 20% x 7 u
=
20100 x 7 u
= 1.4 u
Total number of children at the museum in the end
= 7 u + 1.4 u
= 8.4 u
= 8.4 x 70
= 588
Increase in the number of girls
= 98 - 49
= 49
Total number of girls in the end
= 2 u + 49
= 2 x 70 + 49
= 189
Percentage of children who were girls
=
189588 x 100
= 32
17%
Answer(s): (a) 140; (b) 32
17%