Valen, Dylan and Jack shared a bag of cards. Dylan took 27 as many cards as Jack. Valen took four times as many cards as the total Dylan and Jack took. After Valen had given 54 to Dylan and 30 to Jack, Dylan gave 2 to Jack. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Valen and Dylan had at first.
| |
Dylan |
Jack |
Valen |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 54 |
|
- 54 |
|
| Change 2 |
|
+ 30 |
- 30 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of cards that Dylan and Jack had at first
= 2 u + 7 u
= 15 u
Number of cards that Valen had at first
= 4 x 15 u
= 36 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 45 is 45.
Number of cards that Jack received from Dylan and Valen
= 15 u - 7 u
= 8 u
8 u = 30 + 2
8 u = 32
1 u = 32 ÷ 8 = 4
Difference between the number cards that Valen and Dylan had at first
= 36 u - 2 u
= 34 u
= 34 x 4
= 136
Answer(s): 136
