Nick, Luke and Will shared a bag of stamps. Luke took 27 as many stamps as Will. Nick took twice as many stamps as the total Luke and Will took. After Nick had given 72 to Luke and 9 to Will, Luke gave 9 to Will. In the end, all three of them had the same number of stamps. Find the difference between the number of stamps that Nick and Luke had at first.
| |
Luke |
Will |
Nick |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 72 |
|
- 72 |
|
| Change 2 |
|
+ 9 |
- 9 |
|
| Change 3 |
- 9 |
+ 9 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of stamps that Luke and Will had at first
= 2 u + 7 u
= 9 u
Number of stamps that Nick had at first
= 2 x 9 u
= 18 u
The total number of stamps remains unchanged. Make the total number of stamps the same. LCM of 3 and 27 is 27.
Number of stamps that Will received from Luke and Nick
= 9 u - 7 u
= 2 u
2 u = 9 + 9
2 u = 18
1 u = 18 ÷ 2 = 9
Difference between the number stamps that Nick and Luke had at first
= 18 u - 2 u
= 16 u
= 16 x 9
= 144
Answer(s): 144
