At first, Mark, Eric and Archie had the same amount of money. After Archie spent some of his money, Mark spent ²₇ of his money and Eric spent ¹₂ of his money, Mark had $54 more than Eric. In the end, the total amount of money the three boys had left was $447. How much money did Archie spend?

	Mark	Eric	Archie	Total
Before	7x2 =  14 u	2x7 = 14 u	14 u
Change	- 2x2 = - 4 u	- 1x7 = - 7 u	- ?
After	5x2 = 10 u	1x7 = 7 u		$447

The amount that Mark and Eric each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 2 is 14.

Amount that Mark had more than Eric in the end
= 10 u - 7 u
= 3 u

3 u = 54

1 u = 54 ÷ 3 = 18

Amount that Mark and Eric had in the end
= 10 u + 7 u
= 17 u
= 17 x 18
= $306

Amount that Archie had in the end
= 447 - 306
= $141

Amount that Archie had at first
= 14 u
= 14 x 18
= $252

Amount that Archie spent
= 252 - 141
= $111

Answer(s): $111