Zane, Luke and Tim shared a sum of money. The amount received by Luke was ²₃ the amount of money received by Tim. After Zane had given $46 to Luke and $22 to Tim, Luke gave $4 to Tim. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Zane and Luke had at first.

	Zane	Luke	Tim
Before	2 u + 110	2 u	3 u
Change 1	- 46	+ 46
Change 2	- 22		+ 22
Change 3		- 4	+ 4
After	2 u + 42	2 u + 42	3 u + 26

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

Amount that Tim had in the end = 3 u + 26

Amount that Zane had at first 
= 2 u + 42 + 46 + 22
= 2 u + 110

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

2 u + 42 = 3 u + 26
3 u - 2 u = 42 - 26

1 u = 16

Amount that Zane and Luke had in the end is the same.

Amount that Zane had in the end
= 2 u + 42
= 2 x 16 + 42
= 32 + 42
= $74

Amount that Zane had at first
= 74 + 46 + 22
= $142

Difference in the amounts between Zane and Luke at first
= 142 - 32
= $110

Answer(s): $110