Xuan had $490 less than Andy. Xuan spent ¹₅ of her money and Andy spent ²₃ of his money. In the end, Andy and Xuan had the same amount of money left. Find the amount of money Andy had at first.

	Xuan	Andy	Difference
Before	5x1 = 5 u	3x4 = 12 u	7 u
Change	- 1x1 = - 1 u	- 2x4 = - 8 u
After	4x1 = 4 u	1x4 = 4 u

Fraction of Xuan's money left
= 1 - ¹₅
= ⁴₅

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

Andy and Xuan had the same amount of money in the end. Make the numerators the same. LCM of 4 and 1 is 4.

⁴₅ of Xuan's money = ¹₃ of Andy's money
⁴₅ of Xuan's money = ⁴₁₂ of Andy's money

Amount that Xuan had at first = 5 u
Amount that Andy had at first = 12 u

Amount that Xuan had less than Andy had at first
= 12 u - 5 u
= 7 u

7 u = 490

1 u = 490 ÷ 7 = 70

Amount that Andy had at first
= 12 u
= 12 x 70
= $840

Answer(s): $840