Wesley, Peter and Zeph shared a bag of beads. Peter took 35 as many beads as Zeph. Wesley took twice as many beads as the total Peter and Zeph took. After Wesley had given 30 to Peter and 2 to Zeph, Peter gave 10 to Zeph. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Wesley and Peter had at first.
| |
Peter |
Zeph |
Wesley |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 30 |
|
- 30 |
|
| Change 2 |
|
+ 2 |
- 2 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of beads that Peter and Zeph had at first
= 3 u + 5 u
= 8 u
Number of beads that Wesley had at first
= 2 x 8 u
= 16 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 24 is 24.
Number of beads that Zeph received from Peter and Wesley
= 8 u - 5 u
= 3 u
3 u = 2 + 10
3 u = 12
1 u = 12 ÷ 3 = 4
Difference between the number beads that Wesley and Peter had at first
= 16 u - 3 u
= 13 u
= 13 x 4
= 52
Answer(s): 52
