Kathy had $418 less than Seth. Kathy spent ¹₇ of her money and Seth spent ²₃ of his money. In the end, Seth and Kathy had the same amount of money left. Find the amount of money Seth had at first.

	Kathy	Seth	Difference
Before	7x1 = 7 u	3x6 = 18 u	11 u
Change	- 1x1 = - 1 u	- 2x6 = - 12 u
After	6x1 = 6 u	1x6 = 6 u

Fraction of Kathy's money left
= 1 - ¹₇
= ⁶₇

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

Seth and Kathy had the same amount of money in the end. Make the numerators the same. LCM of 6 and 1 is 6.

⁶₇ of Kathy's money = ¹₃ of Seth's money
⁶₇ of Kathy's money = ⁶₁₈ of Seth's money

Amount that Kathy had at first = 7 u
Amount that Seth had at first = 18 u

Amount that Kathy had less than Seth had at first
= 18 u - 7 u
= 11 u

11 u = 418

1 u = 418 ÷ 11 = 38

Amount that Seth had at first
= 18 u
= 18 x 38
= $684

Answer(s): $684