At first, the ratio of the number of boys to the number of girls at a museum was 3 : 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 26%.
- 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 |
3 u |
7 u |
10 u |
(+ 133) |
+ 0.7 u (+ 49) |
+ 2.6 u (+ 182) |
3 u + 133 |
7.7 u |
12.6 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
= 3 u
= 3 x 70
= 210
(b)
Increase in the number of children
= 26% x 10 u
=
26100 x 10 u
= 2.6 u
Total number of children at the museum in the end
= 10 u + 2.6 u
= 12.6 u
= 12.6 x 70
= 882
Increase in the number of boys
= 182 - 49
= 133
Total number of boys in the end
= 3 u + 133
= 3 x 70 + 133
= 343
Percentage of children who were boys
=
343882 x 100
= 38
89%
Answer(s): (a) 210; (b) 38
89%