Tom, Carl and David have some pens. The ratios of their pens are as follows:
Tom : (Tom + Carl + David) = 1 : 5
Carl : (Tom + David) = 1 : 3
David has 18 pens more than Carl. In the end, David gives away all he has to Carl and Tom so that both Carl and Tom end up with the same number of pens, how many pens has Tom received from David?
Carl |
David |
Tom |
Total |
4x4 |
1x4 |
5x4 |
1x5 |
3x5 |
4x5 |
5 u |
11 u |
4 u |
20 u |
The total number of pens is repeated. Make the total number of pens the same. LCM of 5 and 4 is 20.
Number of pens that David has more than Carl
= 11 u - 5 u
= 6 u
6 u = 18
1 u = 18 ÷ 6 = 3
|
Carl |
David |
Tom |
Before |
5 u |
11 u |
4 u |
Change |
+ 5 u |
- 11 u |
+ 6 u |
After |
10 u |
0 u |
10 u |
Number of pens that Tom has received from David
= 10 u - 4 u
= 6 u
= 6 x 3
= 18
Answer(s): 18