Japheth, Peter and Vaidev shared a bag of stamps. Peter took 27 as many stamps as Vaidev. Japheth took four times as many stamps as the total Peter and Vaidev took. After Japheth had given 114 to Peter and 54 to Vaidev, Peter gave 10 to Vaidev. In the end, all three of them had the same number of stamps. Find the difference between the number of stamps that Japheth and Peter had at first.
| |
Peter |
Vaidev |
Japheth |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 114 |
|
- 114 |
|
| Change 2 |
|
+ 54 |
- 54 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of stamps that Peter and Vaidev had at first
= 2 u + 7 u
= 15 u
Number of stamps that Japheth 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 Vaidev received from Peter and Japheth
= 15 u - 7 u
= 8 u
8 u = 54 + 10
8 u = 64
1 u = 64 ÷ 8 = 8
Difference between the number stamps that Japheth and Peter had at first
= 36 u - 2 u
= 34 u
= 34 x 8
= 272
Answer(s): 272
