Will, Luke and Michael had the same number of beads. Michael gave 0.6 of his beads to Luke. Then Luke gave 0.35 of his beads to Will. Finally, after Luke gave 32 beads to Michael, he had the same number of beads as Michael. How many beads did Michael have at first?
| |
Will |
Luke |
Michael |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.6 u |
- 0.6 u |
| After 1 |
1 u |
1.6 u |
0.4 u |
| Change 2 |
+ 0.56 u |
- 0.56 u |
|
| After 2 |
1.56 u |
1.04 u |
0.4 u |
| Change 3 |
|
- 32 |
+ 32 |
| After 3 |
1.56 u |
1.04 u - 32 |
0.4 u + 32 |
Number of beads that Luke gave to Will
= 0.35 x 1.6 u
= 0.56 u
The number of beads that Luke and Michael had in the end is the same.
1.04 u - 32 = 0.4 u + 32
1.04 u - 0.4 u = 32 + 32
0.64 u = 64
1 u = 64 ÷ 0.64 = 100
Number of beads that Michael had at first
= 1 u
= 100
Answer(s): 100
