Marion had $590 less than Ivan. Marion spent ¹₃ of her money and Ivan spent ⁴₇ of his money. In the end, Ivan and Marion had the same amount of money left. Find the amount of money Ivan had at first.

	Marion	Ivan	Difference
Before	3x3 = 9 u	7x2 = 14 u	5 u
Change	- 1x3 = - 3 u	- 4x2 = - 8 u
After	2x3 = 6 u	3x2 = 6 u

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

Fraction of Ivan's money left
= 1 - ⁴₇
= ³₇

Ivan and Marion had the same amount of money in the end. Make the numerators the same. LCM of 2 and 3 is 6.

²₃ of Marion's money = ³₇ of Ivan's money
⁶₉ of Marion's money = ⁶₁₄ of Ivan's money

Amount that Marion had at first = 9 u
Amount that Ivan had at first = 14 u

Amount that Marion had less than Ivan had at first
= 14 u - 9 u
= 5 u

5 u = 590

1 u = 590 ÷ 5 = 118

Amount that Ivan had at first
= 14 u
= 14 x 118
= $1652

Answer(s): $1652