Riordan, Luke and Archie shared a bag of cards. Luke took 25 as many cards as Archie. Riordan took twice as many cards as the total Luke and Archie took. After Riordan had given 41 to Luke and 8 to Archie, Luke gave 6 to Archie. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Riordan and Luke had at first.
| |
Luke |
Archie |
Riordan |
Total |
| Before |
2 u |
5 u |
14 u |
21 u |
| Change 1 |
+ 41 |
|
- 41 |
|
| Change 2 |
|
+ 8 |
- 8 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x7 =
7 u |
1x7 =
7 u |
1x7 =
7 u |
3x7 =
21 u |
Total number of cards that Luke and Archie had at first
= 2 u + 5 u
= 7 u
Number of cards that Riordan had at first
= 2 x 7 u
= 14 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 21 is 21.
Number of cards that Archie received from Luke and Riordan
= 7 u - 5 u
= 2 u
2 u = 8 + 6
2 u = 14
1 u = 14 ÷ 2 = 7
Difference between the number cards that Riordan and Luke had at first
= 14 u - 2 u
= 12 u
= 12 x 7
= 84
Answer(s): 84
