Linda had $485 less than Sam. Linda spent ¹₄ of her money and Sam spent ²₃ of his money. In the end, Sam and Linda had the same amount of money left. Find the amount of money Sam had at first.

	Linda	Sam	Difference
Before	4x1 = 4 u	3x3 = 9 u	5 u
Change	- 1x1 = - 1 u	- 2x3 = - 6 u
After	3x1 = 3 u	1x3 = 3 u

Fraction of Linda's money left
= 1 - ¹₄
= ³₄

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

Sam and Linda had the same amount of money in the end. Make the numerators the same. LCM of 3 and 1 is 3.

³₄ of Linda's money = ¹₃ of Sam's money
³₄ of Linda's money = ³₉ of Sam's money

Amount that Linda had at first = 4 u
Amount that Sam had at first = 9 u

Amount that Linda had less than Sam had at first
= 9 u - 4 u
= 5 u

5 u = 485

1 u = 485 ÷ 5 = 97

Amount that Sam had at first
= 9 u
= 9 x 97
= $873

Answer(s): $873