Gwen had $693 less than Zeph. Gwen spent ¹₇ of her money and Zeph spent ²₃ of his money. In the end, Zeph and Gwen had the same amount of money left. Find the amount of money Zeph had at first.

	Gwen	Zeph	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 Gwen's money left
= 1 - ¹₇
= ⁶₇

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

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

⁶₇ of Gwen's money = ¹₃ of Zeph's money
⁶₇ of Gwen's money = ⁶₁₈ of Zeph's money

Amount that Gwen had at first = 7 u
Amount that Zeph had at first = 18 u

Amount that Gwen had less than Zeph had at first
= 18 u - 7 u
= 11 u

11 u = 693

1 u = 693 ÷ 11 = 63

Amount that Zeph had at first
= 18 u
= 18 x 63
= $1134

Answer(s): $1134