Tom, Liam and Caden have some cards. The ratios of their cards are as follows:
Tom : (Tom + Liam + Caden) = 1 : 4
Liam : (Tom + Caden) = 1 : 4
Caden has 84 cards more than Liam. In the end, Caden gives away all he has to Liam and Tom so that both Liam and Tom end up with the same number of cards, how many cards has Tom received from Caden?
Liam |
Caden |
Tom |
Total |
3x5 |
1x5 |
4x5 |
1x4 |
4x4 |
5x4 |
4 u |
11 u |
5 u |
20 u |
The total number of cards is repeated. Make the total number of cards the same. LCM of 4 and 5 is 20.
Number of cards that Caden has more than Liam
= 11 u - 4 u
= 7 u
7 u = 84
1 u = 84 ÷ 7 = 12
|
Liam |
Caden |
Tom |
Before |
4 u |
11 u |
5 u |
Change |
+ 6 u |
- 11 u |
+ 5 u |
After |
10 u |
0 u |
10 u |
Number of cards that Tom has received from Caden
= 10 u - 5 u
= 5 u
= 5 x 12
= 60
Answer(s): 60