Warren, Daniel and Ben shared a bag of beads. Daniel took 27 as many beads as Ben. Warren took twice as many beads as the total Daniel and Ben took. After Warren had given 63 to Daniel and 9 to Ben, Daniel gave 7 to Ben. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Warren and Daniel had at first.
| |
Daniel |
Ben |
Warren |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 63 |
|
- 63 |
|
| Change 2 |
|
+ 9 |
- 9 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of beads that Daniel and Ben had at first
= 2 u + 7 u
= 9 u
Number of beads that Warren had at first
= 2 x 9 u
= 18 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 27 is 27.
Number of beads that Ben received from Daniel and Warren
= 9 u - 7 u
= 2 u
2 u = 9 + 7
2 u = 16
1 u = 16 ÷ 2 = 8
Difference between the number beads that Warren and Daniel had at first
= 18 u - 2 u
= 16 u
= 16 x 8
= 128
Answer(s): 128
