Billy, Luis and Will shared a sum of money. The amount received by Luis was ³₄ the amount of money received by Will. After Billy had given $52 to Luis and $23 to Will, Luis gave $8 to Will. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Billy and Luis had at first.

	Billy	Luis	Will
Before	3 u + 119	3 u	4 u
Change 1	- 52	+ 52
Change 2	- 23		+ 23
Change 3		- 8	+ 8
After	3 u + 44	3 u + 44	4 u + 31

Amount that Luis had in the end = 3 u + 44 

Amount that Will had in the end = 4 u + 31

Amount that Billy had at first 
= 3 u + 44 + 52 + 23
= 3 u + 119

Amount that Luis and Will had in the end is the same.

3 u + 44 = 4 u + 31
4 u - 3 u = 44 - 31

1 u = 13

Amount that Billy and Luis had in the end is the same.

Amount that Billy had in the end
= 3 u + 44
= 3 x 13 + 44
= 39 + 44
= $83

Amount that Billy had at first
= 83 + 52 + 23
= $158

Difference in the amounts between Billy and Luis at first
= 158 - 39
= $119

Answer(s): $119