At first, Mark, Tom and Ryan had the same amount of money. After Ryan spent some of his money, Mark spent ⁴₇ of his money and Tom spent ²₃ of his money, Mark had $52 more than Tom. In the end, the total amount of money the three boys had left was $448. How much money did Ryan spend?

	Mark	Tom	Ryan	Total
Before	7x3 =  21 u	3x7 = 21 u	21 u
Change	- 4x3 = - 12 u	- 2x7 = - 14 u	- ?
After	3x3 = 9 u	1x7 = 7 u		$448

The amount that Mark and Tom each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 3 is 21.

Amount that Mark had more than Tom in the end
= 9 u - 7 u
= 2 u

2 u = 52

1 u = 52 ÷ 2 = 26

Amount that Mark and Tom had in the end
= 9 u + 7 u
= 16 u
= 16 x 26
= $416

Amount that Ryan had in the end
= 448 - 416
= $32

Amount that Ryan had at first
= 21 u
= 21 x 26
= $546

Amount that Ryan spent
= 546 - 32
= $514

Answer(s): $514