Luke, Glen and Owen had the same number of beads. Owen gave 0.5 of his beads to Glen. Then Glen gave 0.15 of his beads to Luke. Finally, after Glen gave 31 beads to Owen, he had the same number of beads as Owen. How many beads did Owen have at first?
| |
Luke |
Glen |
Owen |
| 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 Glen gave to Luke
= 0.15 x 1.5 u
= 0.225 u
The number of beads that Glen and Owen 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 Owen had at first
= 1 u
= 80
Answer(s): 80
