At first, David, Pierre and Billy had the same amount of money. After Billy spent some of his money, David spent ⁴₇ of his money and Pierre spent ³₄ of his money, David had $135 more than Pierre. In the end, the total amount of money the three boys had left was $613. How much money did Billy spend?

	David	Pierre	Billy	Total
Before	7x4 =  28 u	4x7 = 28 u	28 u
Change	- 4x4 = - 16 u	- 3x7 = - 21 u	- ?
After	3x4 = 12 u	1x7 = 7 u		$613

The amount that David and Pierre each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 4 is 28.

Amount that David had more than Pierre in the end
= 12 u - 7 u
= 5 u

5 u = 135

1 u = 135 ÷ 5 = 27

Amount that David and Pierre had in the end
= 12 u + 7 u
= 19 u
= 19 x 27
= $513

Amount that Billy had in the end
= 613 - 513
= $100

Amount that Billy had at first
= 28 u
= 28 x 27
= $756

Amount that Billy spent
= 756 - 100
= $656

Answer(s): $656