Winnie had $891 less than Ryan. Winnie spent ¹₇ of her money and Ryan spent ²₃ of his money. In the end, Ryan and Winnie had the same amount of money left. Find the amount of money Ryan had at first.

	Winnie	Ryan	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 Winnie's money left
= 1 - ¹₇
= ⁶₇

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

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

⁶₇ of Winnie's money = ¹₃ of Ryan's money
⁶₇ of Winnie's money = ⁶₁₈ of Ryan's money

Amount that Winnie had at first = 7 u
Amount that Ryan had at first = 18 u

Amount that Winnie had less than Ryan had at first
= 18 u - 7 u
= 11 u

11 u = 891

1 u = 891 ÷ 11 = 81

Amount that Ryan had at first
= 18 u
= 18 x 81
= $1458

Answer(s): $1458