Tim, Gabriel and Archie shared a sum of money. The amount received by Gabriel was ²₃ the amount of money received by Archie. After Tim had given $45 to Gabriel and $27 to Archie, Gabriel gave $3 to Archie. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Tim and Gabriel had at first.

	Tim	Gabriel	Archie
Before	2 u + 114	2 u	3 u
Change 1	- 45	+ 45
Change 2	- 27		+ 27
Change 3		- 3	+ 3
After	2 u + 42	2 u + 42	3 u + 30

Amount that Gabriel had in the end = 2 u + 42 

Amount that Archie had in the end = 3 u + 30

Amount that Tim had at first 
= 2 u + 42 + 45 + 27
= 2 u + 114

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

2 u + 42 = 3 u + 30
3 u - 2 u = 42 - 30

1 u = 12

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

Amount that Tim had in the end
= 2 u + 42
= 2 x 12 + 42
= 24 + 42
= $66

Amount that Tim had at first
= 66 + 45 + 27
= $138

Difference in the amounts between Tim and Gabriel at first
= 138 - 24
= $114

Answer(s): $114