Will, Archie and Lee shared a bag of beads. Archie took 25 as many beads as Lee. Will took twice as many beads as the total Archie and Lee took. After Will had given 57 to Archie and 13 to Lee, Archie gave 7 to Lee. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Will and Archie had at first.
| |
Archie |
Lee |
Will |
Total |
| Before |
2 u |
5 u |
14 u |
21 u |
| Change 1 |
+ 57 |
|
- 57 |
|
| Change 2 |
|
+ 13 |
- 13 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x7 =
7 u |
1x7 =
7 u |
1x7 =
7 u |
3x7 =
21 u |
Total number of beads that Archie and Lee had at first
= 2 u + 5 u
= 7 u
Number of beads that Will had at first
= 2 x 7 u
= 14 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 21 is 21.
Number of beads that Lee received from Archie and Will
= 7 u - 5 u
= 2 u
2 u = 13 + 7
2 u = 20
1 u = 20 ÷ 2 = 10
Difference between the number beads that Will and Archie had at first
= 14 u - 2 u
= 12 u
= 12 x 10
= 120
Answer(s): 120
