At first, the ratio of the number of boys to the number of girls at a museum was 4 : 5. When 52 girls and some boys entered the museum, the number of girls increased by 13% and the total number of children at the museum increased by 25%.
- How many boys were there at first?
- What percentage of the children at the museum were boys in the end? Express your answer as a mixed number.
(a)
Boys |
Girls |
Total |
4 u |
5 u |
9 u |
(+ 128) |
+ 0.65 u (+ 52) |
+ 2.25 u (+ 180) |
4 u + 128 |
5.65 u |
11.25 u |
Number of girls that entered the museum
= 13% x 5 u
=
13100 x 5 u
= 0.65 u
0.65 u = 52
1 u = 52 ÷ 0.65 = 80
Number of boys at first
= 4 u
= 4 x 80
= 320
(b)
Increase in the number of children
= 25% x 9 u
=
25100 x 9 u
= 2.25 u
Total number of children at the museum in the end
= 9 u + 2.25 u
= 11.25 u
= 11.25 x 80
= 900
Increase in the number of boys
= 180 - 52
= 128
Total number of boys in the end
= 4 u + 128
= 4 x 80 + 128
= 448
Percentage of children who were boys
=
448900 x 100
= 49
79%
Answer(s): (a) 320; (b) 49
79%