Perry, Xavier and Warren shared a bag of cards. Xavier took 27 as many cards as Warren. Perry took twice as many cards as the total Xavier and Warren took. After Perry had given 50 to Xavier and 4 to Warren, Xavier gave 8 to Warren. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Perry and Xavier had at first.
| |
Xavier |
Warren |
Perry |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 50 |
|
- 50 |
|
| Change 2 |
|
+ 4 |
- 4 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of cards that Xavier and Warren had at first
= 2 u + 7 u
= 9 u
Number of cards that Perry had at first
= 2 x 9 u
= 18 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 27 is 27.
Number of cards that Warren received from Xavier and Perry
= 9 u - 7 u
= 2 u
2 u = 4 + 8
2 u = 12
1 u = 12 ÷ 2 = 6
Difference between the number cards that Perry and Xavier had at first
= 18 u - 2 u
= 16 u
= 16 x 6
= 96
Answer(s): 96
