Paul, Oscar and Caden shared a bag of buttons. Oscar took 27 as many buttons as Caden. Paul took twice as many buttons as the total Oscar and Caden took. After Paul had given 58 to Oscar and 14 to Caden, Oscar gave 2 to Caden. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Paul and Oscar had at first.
| |
Oscar |
Caden |
Paul |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 58 |
|
- 58 |
|
| Change 2 |
|
+ 14 |
- 14 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of buttons that Oscar and Caden had at first
= 2 u + 7 u
= 9 u
Number of buttons that Paul had at first
= 2 x 9 u
= 18 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 27 is 27.
Number of buttons that Caden received from Oscar and Paul
= 9 u - 7 u
= 2 u
2 u = 14 + 2
2 u = 16
1 u = 16 ÷ 2 = 8
Difference between the number buttons that Paul and Oscar had at first
= 18 u - 2 u
= 16 u
= 16 x 8
= 128
Answer(s): 128
