Xandra had $310 less than Zane. Xandra spent ¹₃ of her money and Zane spent ⁴₇ of his money. In the end, Zane and Xandra had the same amount of money left. Find the amount of money Zane had at first.

	Xandra	Zane	Difference
Before	3x3 = 9 u	7x2 = 14 u	5 u
Change	- 1x3 = - 3 u	- 4x2 = - 8 u
After	2x3 = 6 u	3x2 = 6 u

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

Fraction of Zane's money left
= 1 - ⁴₇
= ³₇

Zane and Xandra had the same amount of money in the end. Make the numerators the same. LCM of 2 and 3 is 6.

²₃ of Xandra's money = ³₇ of Zane's money
⁶₉ of Xandra's money = ⁶₁₄ of Zane's money

Amount that Xandra had at first = 9 u
Amount that Zane had at first = 14 u

Amount that Xandra had less than Zane had at first
= 14 u - 9 u
= 5 u

5 u = 310

1 u = 310 ÷ 5 = 62

Amount that Zane had at first
= 14 u
= 14 x 62
= $868

Answer(s): $868