At first, Lee, Archie and Oliver had the same amount of money. After Oliver spent some of his money, Lee spent ²₇ of his money and Archie spent ³₅ of his money, Lee had $165 more than Archie. In the end, the total amount of money the three boys had left was $735. How much money did Oliver spend?

	Lee	Archie	Oliver	Total
Before	7x5 =  35 u	5x7 = 35 u	35 u
Change	- 2x5 = - 10 u	- 3x7 = - 21 u	- ?
After	5x5 = 25 u	2x7 = 14 u		$735

The amount that Lee and Archie each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 5 is 35.

Amount that Lee had more than Archie in the end
= 25 u - 14 u
= 11 u

11 u = 165

1 u = 165 ÷ 11 = 15

Amount that Lee and Archie had in the end
= 25 u + 14 u
= 39 u
= 39 x 15
= $585

Amount that Oliver had in the end
= 735 - 585
= $150

Amount that Oliver had at first
= 35 u
= 35 x 15
= $525

Amount that Oliver spent
= 525 - 150
= $375

Answer(s): $375