Sam, Michael and Jeremy have some cards. The ratios of their cards are as follows:
Sam : (Sam + Michael + Jeremy) = 3 : 7
Michael : (Sam + Jeremy) = 1 : 3
Jeremy has 12 cards more than Michael. In the end, Jeremy gives away all he has to Michael and Sam so that both Michael and Sam end up with the same number of cards, how many cards has Michael received from Jeremy?
Michael |
Jeremy |
Sam |
Total |
4x4 |
3x4 |
7x4 |
1x7 |
3x7 |
4x7 |
7 u |
9 u |
12 u |
28 u |
The total number of cards is repeated. Make the total number of cards the same. LCM of 7 and 4 is 28.
Number of cards that Jeremy has more than Michael
= 9 u - 7 u
= 2 u
2 u = 12
1 u = 12 ÷ 2 = 6
|
Michael |
Jeremy |
Sam |
Before |
7 u |
9 u |
12 u |
Change |
+ 7 u |
- 9 u |
+ 2 u |
After |
14 u |
0 u |
14 u |
Number of cards that Michael has received from Jeremy
= 14 u - 7 u
= 7 u
= 7 x 6
= 42
Answer(s): 42