Dylan, Seth and Julian shared a bag of cards. Seth took 35 as many cards as Julian. Dylan took twice as many cards as the total Seth and Julian took. After Dylan had given 27 to Seth and 5 to Julian, Seth gave 7 to Julian. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Dylan and Seth had at first.
| |
Seth |
Julian |
Dylan |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 27 |
|
- 27 |
|
| Change 2 |
|
+ 5 |
- 5 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of cards that Seth and Julian had at first
= 3 u + 5 u
= 8 u
Number of cards that Dylan had at first
= 2 x 8 u
= 16 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 24 is 24.
Number of cards that Julian received from Seth and Dylan
= 8 u - 5 u
= 3 u
3 u = 5 + 7
3 u = 12
1 u = 12 ÷ 3 = 4
Difference between the number cards that Dylan and Seth had at first
= 16 u - 3 u
= 13 u
= 13 x 4
= 52
Answer(s): 52
