Gwen had $920 less than Cody. Gwen spent ¹₇ of her money and Cody spent ³₅ of his money. In the end, Cody and Gwen had the same amount of money left. Find the amount of money Cody had at first.

	Gwen	Cody	Difference
Before	7x1 = 7 u	5x3 = 15 u	8 u
Change	- 1x1 = - 1 u	- 3x3 = - 9 u
After	6x1 = 6 u	2x3 = 6 u

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

Fraction of Cody's money left
= 1 - ³₅
= ²₅

Cody and Gwen had the same amount of money in the end. Make the numerators the same. LCM of 6 and 2 is 6.

⁶₇ of Gwen's money = ²₅ of Cody's money
⁶₇ of Gwen's money = ⁶₁₅ of Cody's money

Amount that Gwen had at first = 7 u
Amount that Cody had at first = 15 u

Amount that Gwen had less than Cody had at first
= 15 u - 7 u
= 8 u

8 u = 920

1 u = 920 ÷ 8 = 115

Amount that Cody had at first
= 15 u
= 15 x 115
= $1725

Answer(s): $1725