Zoe had $469 less than Mark. Zoe spent ¹₅ of her money and Mark spent ²₃ of his money. In the end, Mark and Zoe had the same amount of money left. Find the amount of money Mark had at first.

	Zoe	Mark	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 Zoe's money left
= 1 - ¹₅
= ⁴₅

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

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

⁴₅ of Zoe's money = ¹₃ of Mark's money
⁴₅ of Zoe's money = ⁴₁₂ of Mark's money

Amount that Zoe had at first = 5 u
Amount that Mark had at first = 12 u

Amount that Zoe had less than Mark had at first
= 12 u - 5 u
= 7 u

7 u = 469

1 u = 469 ÷ 7 = 67

Amount that Mark had at first
= 12 u
= 12 x 67
= $804

Answer(s): $804