Henry, Luke and John shared a bag of coins. Luke took 27 as many coins as John. Henry took four times as many coins as the total Luke and John took. After Henry had given 125 to Luke and 64 to John, Luke gave 8 to John. In the end, all three of them had the same number of coins. Find the difference between the number of coins that Henry and Luke had at first.
| |
Luke |
John |
Henry |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 125 |
|
- 125 |
|
| Change 2 |
|
+ 64 |
- 64 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of coins that Luke and John had at first
= 2 u + 7 u
= 15 u
Number of coins that Henry had at first
= 4 x 15 u
= 36 u
The total number of coins remains unchanged. Make the total number of coins the same. LCM of 3 and 45 is 45.
Number of coins that John received from Luke and Henry
= 15 u - 7 u
= 8 u
8 u = 64 + 8
8 u = 72
1 u = 72 ÷ 8 = 9
Difference between the number coins that Henry and Luke had at first
= 36 u - 2 u
= 34 u
= 34 x 9
= 306
Answer(s): 306
