At first, Fabian, Archie and Ben had the same amount of money. After Ben spent some of his money, Fabian spent ³₈ of his money and Archie spent ³₄ of his money, Fabian had $75 more than Archie. In the end, the total amount of money the three boys had left was $326. How much money did Ben spend?

	Fabian	Archie	Ben	Total
Before	8x1 =  8 u	4x2 = 8 u	8 u
Change	- 3x1 = - 3 u	- 3x2 = - 6 u	- ?
After	5x1 = 5 u	1x2 = 2 u		$326

The amount that Fabian and Archie each had at first is the same.  Make the amount that they each had the same.  LCM of 8 and 4 is 8.

Amount that Fabian had more than Archie in the end
= 5 u - 2 u
= 3 u

3 u = 75

1 u = 75 ÷ 3 = 25

Amount that Fabian and Archie had in the end
= 5 u + 2 u
= 7 u
= 7 x 25
= $175

Amount that Ben had in the end
= 326 - 175
= $151

Amount that Ben had at first
= 8 u
= 8 x 25
= $200

Amount that Ben spent
= 200 - 151
= $49

Answer(s): $49