Mark, Ian and Howard shared a bag of cards. Ian took 37 as many cards as Howard. Mark took twice as many cards as the total Ian and Howard took. After Mark had given 36 to Ian and 4 to Howard, Ian gave 8 to Howard. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Mark and Ian had at first.
| |
Ian |
Howard |
Mark |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 36 |
|
- 36 |
|
| Change 2 |
|
+ 4 |
- 4 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of cards that Ian and Howard had at first
= 3 u + 7 u
= 10 u
Number of cards that Mark 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 Howard received from Ian and Mark
= 10 u - 7 u
= 3 u
3 u = 4 + 8
3 u = 12
1 u = 12 ÷ 3 = 4
Difference between the number cards that Mark and Ian had at first
= 20 u - 3 u
= 17 u
= 17 x 4
= 68
Answer(s): 68
