Riordan, Archie and Ryan shared a sum of money. The amount received by Archie was ³₄ the amount of money received by Ryan. After Riordan had given $46 to Archie and $25 to Ryan, Archie gave $3 to Ryan. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Riordan and Archie had at first.

	Riordan	Archie	Ryan
Before	3 u + 114	3 u	4 u
Change 1	- 46	+ 46
Change 2	- 25		+ 25
Change 3		- 3	+ 3
After	3 u + 43	3 u + 43	4 u + 28

Amount that Archie had in the end = 3 u + 43 

Amount that Ryan had in the end = 4 u + 28

Amount that Riordan had at first 
= 3 u + 43 + 46 + 25
= 3 u + 114

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

3 u + 43 = 4 u + 28
4 u - 3 u = 43 - 28

1 u = 15

Amount that Riordan and Archie had in the end is the same.

Amount that Riordan had in the end
= 3 u + 43
= 3 x 15 + 43
= 45 + 43
= $88

Amount that Riordan had at first
= 88 + 46 + 25
= $159

Difference in the amounts between Riordan and Archie at first
= 159 - 45
= $114

Answer(s): $114