Will, Mark and Sam shared a bag of marbles. Mark took 27 as many marbles as Sam. Will took twice as many marbles as the total Mark and Sam took. After Will had given 58 to Mark and 14 to Sam, Mark gave 2 to Sam. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Will and Mark had at first.
| |
Mark |
Sam |
Will |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 58 |
|
- 58 |
|
| Change 2 |
|
+ 14 |
- 14 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of marbles that Mark and Sam had at first
= 2 u + 7 u
= 9 u
Number of marbles that Will had at first
= 2 x 9 u
= 18 u
The total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 27 is 27.
Number of marbles that Sam received from Mark and Will
= 9 u - 7 u
= 2 u
2 u = 14 + 2
2 u = 16
1 u = 16 ÷ 2 = 8
Difference between the number marbles that Will and Mark had at first
= 18 u - 2 u
= 16 u
= 16 x 8
= 128
Answer(s): 128
