Sean, Valen and Ian shared a bag of beads. Valen took 27 as many beads as Ian. Sean took four times as many beads as the total Valen and Ian took. After Sean had given 60 to Valen and 24 to Ian, Valen gave 8 to Ian. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Sean and Valen had at first.
| |
Valen |
Ian |
Sean |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 60 |
|
- 60 |
|
| Change 2 |
|
+ 24 |
- 24 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of beads that Valen and Ian had at first
= 2 u + 7 u
= 15 u
Number of beads that Sean had at first
= 4 x 15 u
= 36 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 45 is 45.
Number of beads that Ian received from Valen and Sean
= 15 u - 7 u
= 8 u
8 u = 24 + 8
8 u = 32
1 u = 32 ÷ 8 = 4
Difference between the number beads that Sean and Valen had at first
= 36 u - 2 u
= 34 u
= 34 x 4
= 136
Answer(s): 136
