Caden, Mark and Ben had some stamps in the ratio of 2 : 3 : 5. Ben gave 40% of his stamps to Caden and Mark. As a result, Caden had the same number of stamps as Mark and Ben had 12 fewer stamps than Caden.
- What was the percentage increase in Caden's stamps after receiving from Ben?
- How many stamps did Mark have at first?
| Caden |
Mark |
Ben |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of stamps that Ben gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of stamps that Caden and Mark each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of stamps that Caden had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Caden's stamps after receiving from Ben
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 12
3.5 u - 3 u = 12
0.5 u = 12
1 u = 12 ÷ 0.5 = 24
Number of stamps that Mark had at first
= 3 u
= 3 x 24
= 72
Answer(s): (a) 75%; (b) 72
