Mark, Elijah and Daniel shared a bag of pens. Elijah took 27 as many pens as Daniel. Mark took four times as many pens as the total Elijah and Daniel took. After Mark had given 134 to Elijah and 76 to Daniel, Elijah gave 4 to Daniel. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Mark and Elijah had at first.
| |
Elijah |
Daniel |
Mark |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 134 |
|
- 134 |
|
| Change 2 |
|
+ 76 |
- 76 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of pens that Elijah and Daniel had at first
= 2 u + 7 u
= 15 u
Number of pens that Mark had at first
= 4 x 15 u
= 36 u
The total number of pens remains unchanged. Make the total number of pens the same. LCM of 3 and 45 is 45.
Number of pens that Daniel received from Elijah and Mark
= 15 u - 7 u
= 8 u
8 u = 76 + 4
8 u = 80
1 u = 80 ÷ 8 = 10
Difference between the number pens that Mark and Elijah had at first
= 36 u - 2 u
= 34 u
= 34 x 10
= 340
Answer(s): 340
