Valen, Justin and Simon shared a sum of money. The amount received by Justin was ⁴₅ the amount of money received by Simon. After Valen had given $43 to Justin and $20 to Simon, Justin gave $6 to Simon. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Valen and Justin had at first.

	Valen	Justin	Simon
Before	4 u + 100	4 u	5 u
Change 1	- 43	+ 43
Change 2	- 20		+ 20
Change 3		- 6	+ 6
After	4 u + 37	4 u + 37	5 u + 26

Amount that Justin had in the end = 4 u + 37 

Amount that Simon had in the end = 5 u + 26

Amount that Valen had at first 
= 4 u + 37 + 43 + 20
= 4 u + 100

Amount that Justin and Simon had in the end is the same.

4 u + 37 = 5 u + 26
5 u - 4 u = 37 - 26

1 u = 11

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

Amount that Valen had in the end
= 4 u + 37
= 4 x 11 + 37
= 44 + 37
= $81

Amount that Valen had at first
= 81 + 43 + 20
= $144

Difference in the amounts between Valen and Justin at first
= 144 - 44
= $100

Answer(s): $100