Pierre, Sam and Tom shared a bag of buttons. Sam took 35 as many buttons as Tom. Pierre took twice as many buttons as the total Sam and Tom took. After Pierre had given 38 to Sam and 10 to Tom, Sam gave 8 to Tom. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Pierre and Sam had at first.
| |
Sam |
Tom |
Pierre |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 38 |
|
- 38 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of buttons that Sam and Tom had at first
= 3 u + 5 u
= 8 u
Number of buttons that Pierre had at first
= 2 x 8 u
= 16 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 24 is 24.
Number of buttons that Tom received from Sam and Pierre
= 8 u - 5 u
= 3 u
3 u = 10 + 8
3 u = 18
1 u = 18 ÷ 3 = 6
Difference between the number buttons that Pierre and Sam had at first
= 16 u - 3 u
= 13 u
= 13 x 6
= 78
Answer(s): 78
