Owen, Wesley and Mark shared a bag of cards. Wesley took 27 as many cards as Mark. Owen took thrice as many cards as the total Wesley and Mark took. After Owen had given 104 to Wesley and 46 to Mark, Wesley gave 4 to Mark. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Owen and Wesley had at first.
| |
Wesley |
Mark |
Owen |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 104 |
|
- 104 |
|
| Change 2 |
|
+ 46 |
- 46 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of cards that Wesley and Mark had at first
= 2 u + 7 u
= 12 u
Number of cards that Owen had at first
= 3 x 12 u
= 27 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 36 is 36.
Number of cards that Mark received from Wesley and Owen
= 12 u - 7 u
= 5 u
5 u = 46 + 4
5 u = 50
1 u = 50 ÷ 5 = 10
Difference between the number cards that Owen and Wesley had at first
= 27 u - 2 u
= 25 u
= 25 x 10
= 250
Answer(s): 250
