At first, Ethan, Simon and John had the same amount of money. After John spent some of his money, Ethan spent ²₇ of his money and Simon spent ²₃ of his money, Ethan had $152 more than Simon. In the end, the total amount of money the three boys had left was $550. How much money did John spend?

	Ethan	Simon	John	Total
Before	7x3 =  21 u	3x7 = 21 u	21 u
Change	- 2x3 = - 6 u	- 2x7 = - 14 u	- ?
After	5x3 = 15 u	1x7 = 7 u		$550

The amount that Ethan and Simon 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 Ethan had more than Simon in the end
= 15 u - 7 u
= 8 u

8 u = 152

1 u = 152 ÷ 8 = 19

Amount that Ethan and Simon had in the end
= 15 u + 7 u
= 22 u
= 22 x 19
= $418

Amount that John had in the end
= 550 - 418
= $132

Amount that John had at first
= 21 u
= 21 x 19
= $399

Amount that John spent
= 399 - 132
= $267

Answer(s): $267