At first, Archie, Warren and Cole had the same amount of money. After Cole spent some of his money, Archie spent ³₅ of his money and Warren spent ³₄ of his money, Archie had $84 more than Warren. In the end, the total amount of money the three boys had left was $434. How much money did Cole spend?

	Archie	Warren	Cole	Total
Before	5x4 =  20 u	4x5 = 20 u	20 u
Change	- 3x4 = - 12 u	- 3x5 = - 15 u	- ?
After	2x4 = 8 u	1x5 = 5 u		$434

The amount that Archie and Warren each had at first is the same.  Make the amount that they each had the same.  LCM of 5 and 4 is 20.

Amount that Archie had more than Warren in the end
= 8 u - 5 u
= 3 u

3 u = 84

1 u = 84 ÷ 3 = 28

Amount that Archie and Warren had in the end
= 8 u + 5 u
= 13 u
= 13 x 28
= $364

Amount that Cole had in the end
= 434 - 364
= $70

Amount that Cole had at first
= 20 u
= 20 x 28
= $560

Amount that Cole spent
= 560 - 70
= $490

Answer(s): $490