Xandra had $159 less than Jack. Xandra spent ¹₃ of her money and Jack spent ²₃ of his money. In the end, Jack and Xandra had the same amount of money left. Find the amount of money Jack had at first.

	Xandra	Jack	Difference
Before	3x1 = 3 u	3x2 = 6 u	3 u
Change	- 1x1 = - 1 u	- 2x2 = - 4 u
After	2x1 = 2 u	1x2 = 2 u

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

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

Jack and Xandra had the same amount of money in the end. Make the numerators the same. LCM of 2 and 1 is 2.

²₃ of Xandra's money = ¹₃ of Jack's money
²₃ of Xandra's money = ²₆ of Jack's money

Amount that Xandra had at first = 3 u
Amount that Jack had at first = 6 u

Amount that Xandra had less than Jack had at first
= 6 u - 3 u
= 3 u

3 u = 159

1 u = 159 ÷ 3 = 53

Amount that Jack had at first
= 6 u
= 6 x 53
= $318

Answer(s): $318