Andy, Ryan and Ben shared a bag of cards. Ryan took 37 as many cards as Ben. Andy took twice as many cards as the total Ryan and Ben took. After Andy had given 76 to Ryan and 24 to Ben, Ryan gave 6 to Ben. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Andy and Ryan had at first.
| |
Ryan |
Ben |
Andy |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 76 |
|
- 76 |
|
| Change 2 |
|
+ 24 |
- 24 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of cards that Ryan and Ben had at first
= 3 u + 7 u
= 10 u
Number of cards that Andy had at first
= 2 x 10 u
= 20 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 30 is 30.
Number of cards that Ben received from Ryan and Andy
= 10 u - 7 u
= 3 u
3 u = 24 + 6
3 u = 30
1 u = 30 ÷ 3 = 10
Difference between the number cards that Andy and Ryan had at first
= 20 u - 3 u
= 17 u
= 17 x 10
= 170
Answer(s): 170
