At first, Dylan, Tim and Liam had the same amount of money. After Liam spent some of his money, Dylan spent ²₅ of his money and Tim spent ³₄ of his money, Dylan had $189 more than Tim. In the end, the total amount of money the three boys had left was $522. How much money did Liam spend?

	Dylan	Tim	Liam	Total
Before	5x4 =  20 u	4x5 = 20 u	20 u
Change	- 2x4 = - 8 u	- 3x5 = - 15 u	- ?
After	3x4 = 12 u	1x5 = 5 u		$522

The amount that Dylan and Tim 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 Dylan had more than Tim in the end
= 12 u - 5 u
= 7 u

7 u = 189

1 u = 189 ÷ 7 = 27

Amount that Dylan and Tim had in the end
= 12 u + 5 u
= 17 u
= 17 x 27
= $459

Amount that Liam had in the end
= 522 - 459
= $63

Amount that Liam had at first
= 20 u
= 20 x 27
= $540

Amount that Liam spent
= 540 - 63
= $477

Answer(s): $477