Ivan, Mark and Eric shared a bag of pens. Mark took 27 as many pens as Eric. Ivan took twice as many pens as the total Mark and Eric took. After Ivan had given 37 to Mark and 8 to Eric, Mark gave 2 to Eric. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Ivan and Mark had at first.
| |
Mark |
Eric |
Ivan |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 37 |
|
- 37 |
|
| Change 2 |
|
+ 8 |
- 8 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of pens that Mark and Eric had at first
= 2 u + 7 u
= 9 u
Number of pens that Ivan had at first
= 2 x 9 u
= 18 u
The total number of pens remains unchanged. Make the total number of pens the same. LCM of 3 and 27 is 27.
Number of pens that Eric received from Mark and Ivan
= 9 u - 7 u
= 2 u
2 u = 8 + 2
2 u = 10
1 u = 10 ÷ 2 = 5
Difference between the number pens that Ivan and Mark had at first
= 18 u - 2 u
= 16 u
= 16 x 5
= 80
Answer(s): 80
