Archie, Vaidev and Liam had the same number of beads. Liam gave 0.5 of his beads to Vaidev. Then Vaidev gave 0.25 of his beads to Archie. Finally, after Vaidev gave 20 beads to Liam, he had the same number of beads as Liam. How many beads did Liam have at first?
| |
Archie |
Vaidev |
Liam |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.5 u |
- 0.5 u |
| After 1 |
1 u |
1.5 u |
0.5 u |
| Change 2 |
+ 0.375 u |
- 0.375 u |
|
| After 2 |
1.375 u |
1.125 u |
0.5 u |
| Change 3 |
|
- 20 |
+ 20 |
| After 3 |
1.375 u |
1.125 u - 20 |
0.5 u + 20 |
Number of beads that Vaidev gave to Archie
= 0.25 x 1.5 u
= 0.375 u
The number of beads that Vaidev and Liam had in the end is the same.
1.125 u - 20 = 0.5 u + 20
1.125 u - 0.5 u = 20 + 20
0.625 u = 40
1 u = 40 ÷ 0.625 = 64
Number of beads that Liam had at first
= 1 u
= 64
Answer(s): 64
