Zane, Vincent and Ben shared a sum of money. The amount received by Vincent was ²₃ the amount of money received by Ben. After Zane had given $42 to Vincent and $23 to Ben, Vincent gave $7 to Ben. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Zane and Vincent had at first.

	Zane	Vincent	Ben
Before	2 u + 100	2 u	3 u
Change 1	- 42	+ 42
Change 2	- 23		+ 23
Change 3		- 7	+ 7
After	2 u + 35	2 u + 35	3 u + 30

Amount that Vincent had in the end = 2 u + 35 

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

Amount that Zane had at first 
= 2 u + 35 + 42 + 23
= 2 u + 100

Amount that Vincent and Ben had in the end is the same.

2 u + 35 = 3 u + 30
3 u - 2 u = 35 - 30

1 u = 5

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

Amount that Zane had in the end
= 2 u + 35
= 2 x 5 + 35
= 10 + 35
= $45

Amount that Zane had at first
= 45 + 42 + 23
= $110

Difference in the amounts between Zane and Vincent at first
= 110 - 10
= $100

Answer(s): $100