Zeph, Albert and Valen shared a sum of money. The amount received by Albert was ³₄ the amount of money received by Valen. After Zeph had given $45 to Albert and $22 to Valen, Albert gave $5 to Valen. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Zeph and Albert had at first.

	Zeph	Albert	Valen
Before	3 u + 107	3 u	4 u
Change 1	- 45	+ 45
Change 2	- 22		+ 22
Change 3		- 5	+ 5
After	3 u + 40	3 u + 40	4 u + 27

Amount that Albert had in the end = 3 u + 40 

Amount that Valen had in the end = 4 u + 27

Amount that Zeph had at first 
= 3 u + 40 + 45 + 22
= 3 u + 107

Amount that Albert and Valen had in the end is the same.

3 u + 40 = 4 u + 27
4 u - 3 u = 40 - 27

1 u = 13

Amount that Zeph and Albert had in the end is the same.

Amount that Zeph had in the end
= 3 u + 40
= 3 x 13 + 40
= 39 + 40
= $79

Amount that Zeph had at first
= 79 + 45 + 22
= $146

Difference in the amounts between Zeph and Albert at first
= 146 - 39
= $107

Answer(s): $107