Howard, Archie and Brandon shared a sum of money. The amount received by Archie was ³₄ the amount of money received by Brandon. After Howard had given $40 to Archie and $22 to Brandon, Archie gave $2 to Brandon. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Howard and Archie had at first.

	Howard	Archie	Brandon
Before	3 u + 100	3 u	4 u
Change 1	- 40	+ 40
Change 2	- 22		+ 22
Change 3		- 2	+ 2
After	3 u + 38	3 u + 38	4 u + 24

Amount that Archie had in the end = 3 u + 38 

Amount that Brandon had in the end = 4 u + 24

Amount that Howard had at first 
= 3 u + 38 + 40 + 22
= 3 u + 100

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

3 u + 38 = 4 u + 24
4 u - 3 u = 38 - 24

1 u = 14

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

Amount that Howard had in the end
= 3 u + 38
= 3 x 14 + 38
= 42 + 38
= $80

Amount that Howard had at first
= 80 + 40 + 22
= $142

Difference in the amounts between Howard and Archie at first
= 142 - 42
= $100

Answer(s): $100