Cody, Howard and Owen shared a bag of cards. Howard took 27 as many cards as Owen. Cody took thrice as many cards as the total Howard and Owen took. After Cody had given 106 to Howard and 44 to Owen, Howard gave 6 to Owen. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Cody and Howard had at first.
| |
Howard |
Owen |
Cody |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 106 |
|
- 106 |
|
| Change 2 |
|
+ 44 |
- 44 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of cards that Howard and Owen had at first
= 2 u + 7 u
= 12 u
Number of cards that Cody had at first
= 3 x 12 u
= 27 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 36 is 36.
Number of cards that Owen received from Howard and Cody
= 12 u - 7 u
= 5 u
5 u = 44 + 6
5 u = 50
1 u = 50 ÷ 5 = 10
Difference between the number cards that Cody and Howard had at first
= 27 u - 2 u
= 25 u
= 25 x 10
= 250
Answer(s): 250
