At first, Peter, Bryan and Billy had the same amount of money. After Billy spent some of his money, Peter spent ³₅ of his money and Bryan spent ³₄ of his money, Peter had $51 more than Bryan. In the end, the total amount of money the three boys had left was $412. How much money did Billy spend?

	Peter	Bryan	Billy	Total
Before	5x4 =  20 u	4x5 = 20 u	20 u
Change	- 3x4 = - 12 u	- 3x5 = - 15 u	- ?
After	2x4 = 8 u	1x5 = 5 u		$412

The amount that Peter and Bryan 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 Peter had more than Bryan in the end
= 8 u - 5 u
= 3 u

3 u = 51

1 u = 51 ÷ 3 = 17

Amount that Peter and Bryan had in the end
= 8 u + 5 u
= 13 u
= 13 x 17
= $221

Amount that Billy had in the end
= 412 - 221
= $191

Amount that Billy had at first
= 20 u
= 20 x 17
= $340

Amount that Billy spent
= 340 - 191
= $149

Answer(s): $149