Cindy had $365 less than Mark. Cindy spent ¹₃ of her money and Mark spent ⁴₇ of his money. In the end, Mark and Cindy had the same amount of money left. Find the amount of money Mark had at first.

	Cindy	Mark	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 Cindy's money left
= 1 - ¹₃
= ²₃

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

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

²₃ of Cindy's money = ³₇ of Mark's money
⁶₉ of Cindy's money = ⁶₁₄ of Mark's money

Amount that Cindy had at first = 9 u
Amount that Mark had at first = 14 u

Amount that Cindy had less than Mark had at first
= 14 u - 9 u
= 5 u

5 u = 365

1 u = 365 ÷ 5 = 73

Amount that Mark had at first
= 14 u
= 14 x 73
= $1022

Answer(s): $1022