Zeph, Tim and Tom shared a bag of coins. Tim took 37 as many coins as Tom. Zeph took twice as many coins as the total Tim and Tom took. After Zeph had given 52 to Tim and 8 to Tom, Tim gave 10 to Tom. In the end, all three of them had the same number of coins. Find the difference between the number of coins that Zeph and Tim had at first.
| |
Tim |
Tom |
Zeph |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 52 |
|
- 52 |
|
| Change 2 |
|
+ 8 |
- 8 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of coins that Tim and Tom had at first
= 3 u + 7 u
= 10 u
Number of coins that Zeph had at first
= 2 x 10 u
= 20 u
The total number of coins remains unchanged. Make the total number of coins the same. LCM of 3 and 30 is 30.
Number of coins that Tom received from Tim and Zeph
= 10 u - 7 u
= 3 u
3 u = 8 + 10
3 u = 18
1 u = 18 ÷ 3 = 6
Difference between the number coins that Zeph and Tim had at first
= 20 u - 3 u
= 17 u
= 17 x 6
= 102
Answer(s): 102
