Michael, Tim and Liam shared a bag of stamps. Tim took 27 as many stamps as Liam. Michael took four times as many stamps as the total Tim and Liam took. After Michael had given 58 to Tim and 26 to Liam, Tim gave 6 to Liam. In the end, all three of them had the same number of stamps. Find the difference between the number of stamps that Michael and Tim had at first.
| |
Tim |
Liam |
Michael |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 58 |
|
- 58 |
|
| Change 2 |
|
+ 26 |
- 26 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of stamps that Tim and Liam had at first
= 2 u + 7 u
= 15 u
Number of stamps that Michael 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 Liam received from Tim and Michael
= 15 u - 7 u
= 8 u
8 u = 26 + 6
8 u = 32
1 u = 32 ÷ 8 = 4
Difference between the number stamps that Michael and Tim had at first
= 36 u - 2 u
= 34 u
= 34 x 4
= 136
Answer(s): 136
