Ivan, Ben and Ethan shared a bag of cards. Ben took 27 as many cards as Ethan. Ivan took four times as many cards as the total Ben and Ethan took. After Ivan had given 96 to Ben and 51 to Ethan, Ben gave 5 to Ethan. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Ivan and Ben had at first.
| |
Ben |
Ethan |
Ivan |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 96 |
|
- 96 |
|
| Change 2 |
|
+ 51 |
- 51 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of cards that Ben and Ethan had at first
= 2 u + 7 u
= 15 u
Number of cards that Ivan 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 Ethan received from Ben and Ivan
= 15 u - 7 u
= 8 u
8 u = 51 + 5
8 u = 56
1 u = 56 ÷ 8 = 7
Difference between the number cards that Ivan and Ben had at first
= 36 u - 2 u
= 34 u
= 34 x 7
= 238
Answer(s): 238
