George, Sean and Caden shared a bag of beads. Sean took 27 as many beads as Caden. George took twice as many beads as the total Sean and Caden took. After George had given 39 to Sean and 6 to Caden, Sean gave 4 to Caden. In the end, all three of them had the same number of beads. Find the difference between the number of beads that George and Sean had at first.
| |
Sean |
Caden |
George |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 39 |
|
- 39 |
|
| Change 2 |
|
+ 6 |
- 6 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of beads that Sean and Caden had at first
= 2 u + 7 u
= 9 u
Number of beads that George 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 Caden received from Sean and George
= 9 u - 7 u
= 2 u
2 u = 6 + 4
2 u = 10
1 u = 10 ÷ 2 = 5
Difference between the number beads that George and Sean had at first
= 18 u - 2 u
= 16 u
= 16 x 5
= 80
Answer(s): 80
