Dylan, Oliver and Paul shared a bag of beads. Oliver took 27 as many beads as Paul. Dylan took four times as many beads as the total Oliver and Paul took. After Dylan had given 44 to Oliver and 19 to Paul, Oliver gave 5 to Paul. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Dylan and Oliver had at first.
| |
Oliver |
Paul |
Dylan |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 44 |
|
- 44 |
|
| Change 2 |
|
+ 19 |
- 19 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of beads that Oliver and Paul had at first
= 2 u + 7 u
= 15 u
Number of beads that Dylan had at first
= 4 x 15 u
= 36 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 45 is 45.
Number of beads that Paul received from Oliver and Dylan
= 15 u - 7 u
= 8 u
8 u = 19 + 5
8 u = 24
1 u = 24 ÷ 8 = 3
Difference between the number beads that Dylan and Oliver had at first
= 36 u - 2 u
= 34 u
= 34 x 3
= 102
Answer(s): 102
