Mary had $327 less than Peter. Mary spent ¹₃ of her money and Peter spent ²₃ of his money. In the end, Peter and Mary had the same amount of money left. Find the amount of money Peter had at first.

	Mary	Peter	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 Mary's money left
= 1 - ¹₃
= ²₃

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

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

²₃ of Mary's money = ¹₃ of Peter's money
²₃ of Mary's money = ²₆ of Peter's money

Amount that Mary had at first = 3 u
Amount that Peter had at first = 6 u

Amount that Mary had less than Peter had at first
= 6 u - 3 u
= 3 u

3 u = 327

1 u = 327 ÷ 3 = 109

Amount that Peter had at first
= 6 u
= 6 x 109
= $654

Answer(s): $654