Luke, Nick and Owen shared a bag of cards. Nick took 35 as many cards as Owen. Luke took twice as many cards as the total Nick and Owen took. After Luke had given 34 to Nick and 14 to Owen, Nick gave 4 to Owen. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Luke and Nick had at first.
| |
Nick |
Owen |
Luke |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 34 |
|
- 34 |
|
| Change 2 |
|
+ 14 |
- 14 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of cards that Nick and Owen had at first
= 3 u + 5 u
= 8 u
Number of cards that Luke 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 Owen received from Nick and Luke
= 8 u - 5 u
= 3 u
3 u = 14 + 4
3 u = 18
1 u = 18 ÷ 3 = 6
Difference between the number cards that Luke and Nick had at first
= 16 u - 3 u
= 13 u
= 13 x 6
= 78
Answer(s): 78
