Irene had $339 less than Ivan. Irene spent ¹₃ of her money and Ivan spent ²₃ of his money. In the end, Ivan and Irene had the same amount of money left. Find the amount of money Ivan had at first.

	Irene	Ivan	Difference
Before	3x1 = 3 u	3x2 = 6 u	3 u
Change	- 1x1 = - 1 u	- 2x2 = - 4 u
After	2x1 = 2 u	1x2 = 2 u

Fraction of Irene's money left
= 1 - ¹₃
= ²₃

Fraction of Ivan's money left
= 1 - ²₃
= ¹₃

Ivan and Irene had the same amount of money in the end. Make the numerators the same. LCM of 2 and 1 is 2.

²₃ of Irene's money = ¹₃ of Ivan's money
²₃ of Irene's money = ²₆ of Ivan's money

Amount that Irene had at first = 3 u
Amount that Ivan had at first = 6 u

Amount that Irene had less than Ivan had at first
= 6 u - 3 u
= 3 u

3 u = 339

1 u = 339 ÷ 3 = 113

Amount that Ivan had at first
= 6 u
= 6 x 113
= $678

Answer(s): $678