Peter, Jack and Sam shared a bag of stamps. Jack took 27 as many stamps as Sam. Peter took four times as many stamps as the total Jack and Sam took. After Peter had given 32 to Jack and 10 to Sam, Jack gave 6 to Sam. In the end, all three of them had the same number of stamps. Find the difference between the number of stamps that Peter and Jack had at first.
| |
Jack |
Sam |
Peter |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 32 |
|
- 32 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of stamps that Jack and Sam had at first
= 2 u + 7 u
= 15 u
Number of stamps that Peter had at first
= 4 x 15 u
= 36 u
The total number of stamps remains unchanged. Make the total number of stamps the same. LCM of 3 and 45 is 45.
Number of stamps that Sam received from Jack and Peter
= 15 u - 7 u
= 8 u
8 u = 10 + 6
8 u = 16
1 u = 16 ÷ 8 = 2
Difference between the number stamps that Peter and Jack had at first
= 36 u - 2 u
= 34 u
= 34 x 2
= 68
Answer(s): 68
