At first, the ratio of the number of boys to the number of girls at a museum was 4 : 7. When 49 girls and some boys entered the museum, the number of girls increased by 10% and the total number of children at the museum increased by 30%.
- 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 |
7 u |
11 u |
(+ 182) |
+ 0.7 u (+ 49) |
+ 3.3 u (+ 231) |
4 u + 182 |
7.7 u |
14.3 u |
Number of girls that entered the museum
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
0.7 u = 49
1 u = 49 ÷ 0.7 = 70
Number of boys at first
= 4 u
= 4 x 70
= 280
(b)
Increase in the number of children
= 30% x 11 u
=
30100 x 11 u
= 3.3 u
Total number of children at the museum in the end
= 11 u + 3.3 u
= 14.3 u
= 14.3 x 70
= 1001
Increase in the number of boys
= 231 - 49
= 182
Total number of boys in the end
= 4 u + 182
= 4 x 70 + 182
= 462
Percentage of children who were boys
=
4621001 x 100
= 46
213%
Answer(s): (a) 280; (b) 46
213%