At first, Julian, Vincent and Ivan had the same amount of money. After Ivan spent some of his money, Julian spent ²₅ of his money and Vincent spent ²₃ of his money, Julian had $116 more than Vincent. In the end, the total amount of money the three boys had left was $500. How much money did Ivan spend?

	Julian	Vincent	Ivan	Total
Before	5x3 =  15 u	3x5 = 15 u	15 u
Change	- 2x3 = - 6 u	- 2x5 = - 10 u	- ?
After	3x3 = 9 u	1x5 = 5 u		$500

The amount that Julian and Vincent each had at first is the same.  Make the amount that they each had the same.  LCM of 5 and 3 is 15.

Amount that Julian had more than Vincent in the end
= 9 u - 5 u
= 4 u

4 u = 116

1 u = 116 ÷ 4 = 29

Amount that Julian and Vincent had in the end
= 9 u + 5 u
= 14 u
= 14 x 29
= $406

Amount that Ivan had in the end
= 500 - 406
= $94

Amount that Ivan had at first
= 15 u
= 15 x 29
= $435

Amount that Ivan spent
= 435 - 94
= $341

Answer(s): $341