Luis, Ryan and Michael shared a sum of money. The amount received by Ryan was ⁴₅ the amount of money received by Michael. After Luis had given $41 to Ryan and $23 to Michael, Ryan gave $3 to Michael. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Luis and Ryan had at first.

	Luis	Ryan	Michael
Before	4 u + 102	4 u	5 u
Change 1	- 41	+ 41
Change 2	- 23		+ 23
Change 3		- 3	+ 3
After	4 u + 38	4 u + 38	5 u + 26

Amount that Ryan had in the end = 4 u + 38 

Amount that Michael had in the end = 5 u + 26

Amount that Luis had at first 
= 4 u + 38 + 41 + 23
= 4 u + 102

Amount that Ryan and Michael had in the end is the same.

4 u + 38 = 5 u + 26
5 u - 4 u = 38 - 26

1 u = 12

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

Amount that Luis had in the end
= 4 u + 38
= 4 x 12 + 38
= 48 + 38
= $86

Amount that Luis had at first
= 86 + 41 + 23
= $150

Difference in the amounts between Luis and Ryan at first
= 150 - 48
= $102

Answer(s): $102