Vincent, Warren and Rael had the same number of beads. Rael gave 0.5 of his beads to Warren. Then Warren gave 0.15 of his beads to Vincent. Finally, after Warren gave 31 beads to Rael, he had the same number of beads as Rael. How many beads did Rael have at first?
| |
Vincent |
Warren |
Rael |
| 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 |
+ 0.225 u |
- 0.225 u |
|
| After 2 |
1.225 u |
1.275 u |
0.5 u |
| Change 3 |
|
- 31 |
+ 31 |
| After 3 |
1.225 u |
1.275 u - 31 |
0.5 u + 31 |
Number of beads that Warren gave to Vincent
= 0.15 x 1.5 u
= 0.225 u
The number of beads that Warren and Rael had in the end is the same.
1.275 u - 31 = 0.5 u + 31
1.275 u - 0.5 u = 31 + 31
0.775 u = 62
1 u = 62 ÷ 0.775 = 80
Number of beads that Rael had at first
= 1 u
= 80
Answer(s): 80
