At first, Jack, Fred and Archie had the same amount of money. After Archie spent some of his money, Jack spent ³₇ of his money and Fred spent ³₄ of his money, Jack had $90 more than Fred. In the end, the total amount of money the three boys had left was $382. How much money did Archie spend?

	Jack	Fred	Archie	Total
Before	7x4 =  28 u	4x7 = 28 u	28 u
Change	- 3x4 = - 12 u	- 3x7 = - 21 u	- ?
After	4x4 = 16 u	1x7 = 7 u		$382

The amount that Jack and Fred each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 4 is 28.

Amount that Jack had more than Fred in the end
= 16 u - 7 u
= 9 u

9 u = 90

1 u = 90 ÷ 9 = 10

Amount that Jack and Fred had in the end
= 16 u + 7 u
= 23 u
= 23 x 10
= $230

Amount that Archie had in the end
= 382 - 230
= $152

Amount that Archie had at first
= 28 u
= 28 x 10
= $280

Amount that Archie spent
= 280 - 152
= $128

Answer(s): $128