Charlie, Luke and Cole shared a sum of money. The amount received by Luke was ⁴₅ the amount of money received by Cole. After Charlie had given $53 to Luke and $24 to Cole, Luke gave $5 to Cole. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Charlie and Luke had at first.

	Charlie	Luke	Cole
Before	4 u + 125	4 u	5 u
Change 1	- 53	+ 53
Change 2	- 24		+ 24
Change 3		- 5	+ 5
After	4 u + 48	4 u + 48	5 u + 29

Amount that Luke had in the end = 4 u + 48 

Amount that Cole had in the end = 5 u + 29

Amount that Charlie had at first 
= 4 u + 48 + 53 + 24
= 4 u + 125

Amount that Luke and Cole had in the end is the same.

4 u + 48 = 5 u + 29
5 u - 4 u = 48 - 29

1 u = 19

Amount that Charlie and Luke had in the end is the same.

Amount that Charlie had in the end
= 4 u + 48
= 4 x 19 + 48
= 76 + 48
= $124

Amount that Charlie had at first
= 124 + 53 + 24
= $201

Difference in the amounts between Charlie and Luke at first
= 201 - 76
= $125

Answer(s): $125