Owen, Bryan and Zeph shared a bag of cards. Bryan took 27 as many cards as Zeph. Owen took four times as many cards as the total Bryan and Zeph took. After Owen had given 58 to Bryan and 26 to Zeph, Bryan gave 6 to Zeph. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Owen and Bryan had at first.
| |
Bryan |
Zeph |
Owen |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 58 |
|
- 58 |
|
| Change 2 |
|
+ 26 |
- 26 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of cards that Bryan and Zeph had at first
= 2 u + 7 u
= 15 u
Number of cards that Owen 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 Zeph received from Bryan and Owen
= 15 u - 7 u
= 8 u
8 u = 26 + 6
8 u = 32
1 u = 32 ÷ 8 = 4
Difference between the number cards that Owen and Bryan had at first
= 36 u - 2 u
= 34 u
= 34 x 4
= 136
Answer(s): 136
