Fabian, Sam and Ryan shared a sum of money. The amount received by Sam was ⁴₅ the amount of money received by Ryan. After Fabian had given $50 to Sam and $22 to Ryan, Sam gave $5 to Ryan. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Fabian and Sam had at first.

	Fabian	Sam	Ryan
Before	4 u + 117	4 u	5 u
Change 1	- 50	+ 50
Change 2	- 22		+ 22
Change 3		- 5	+ 5
After	4 u + 45	4 u + 45	5 u + 27

Amount that Sam had in the end = 4 u + 45 

Amount that Ryan had in the end = 5 u + 27

Amount that Fabian had at first 
= 4 u + 45 + 50 + 22
= 4 u + 117

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

4 u + 45 = 5 u + 27
5 u - 4 u = 45 - 27

1 u = 18

Amount that Fabian and Sam had in the end is the same.

Amount that Fabian had in the end
= 4 u + 45
= 4 x 18 + 45
= 72 + 45
= $117

Amount that Fabian had at first
= 117 + 50 + 22
= $189

Difference in the amounts between Fabian and Sam at first
= 189 - 72
= $117

Answer(s): $117