Paul, Gabriel and Oscar had the same number of beads. Oscar gave 0.8 of his beads to Gabriel. Then Gabriel gave 0.25 of his beads to Paul. Finally, after Gabriel gave 23 beads to Oscar, he had the same number of beads as Oscar. How many beads did Oscar have at first?
| |
Paul |
Gabriel |
Oscar |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.8 u |
- 0.8 u |
| After 1 |
1 u |
1.8 u |
0.2 u |
| Change 2 |
+ 0.45 u |
- 0.45 u |
|
| After 2 |
1.45 u |
1.35 u |
0.2 u |
| Change 3 |
|
- 23 |
+ 23 |
| After 3 |
1.45 u |
1.35 u - 23 |
0.2 u + 23 |
Number of beads that Gabriel gave to Paul
= 0.25 x 1.8 u
= 0.45 u
The number of beads that Gabriel and Oscar had in the end is the same.
1.35 u - 23 = 0.2 u + 23
1.35 u - 0.2 u = 23 + 23
1.15 u = 46
1 u = 46 ÷ 1.15 = 40
Number of beads that Oscar had at first
= 1 u
= 40
Answer(s): 40
