Archie, Ethan and Gabriel shared a sum of money. The amount received by Ethan was ²₃ the amount of money received by Gabriel. After Archie had given $54 to Ethan and $25 to Gabriel, Ethan gave $4 to Gabriel. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Archie and Ethan had at first.

	Archie	Ethan	Gabriel
Before	2 u + 129	2 u	3 u
Change 1	- 54	+ 54
Change 2	- 25		+ 25
Change 3		- 4	+ 4
After	2 u + 50	2 u + 50	3 u + 29

Amount that Ethan had in the end = 2 u + 50 

Amount that Gabriel had in the end = 3 u + 29

Amount that Archie had at first 
= 2 u + 50 + 54 + 25
= 2 u + 129

Amount that Ethan and Gabriel had in the end is the same.

2 u + 50 = 3 u + 29
3 u - 2 u = 50 - 29

1 u = 21

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

Amount that Archie had in the end
= 2 u + 50
= 2 x 21 + 50
= 42 + 50
= $92

Amount that Archie had at first
= 92 + 54 + 25
= $171

Difference in the amounts between Archie and Ethan at first
= 171 - 42
= $129

Answer(s): $129