Natalie had $108 less than Cole. Natalie spent ¹₃ of her money and Cole spent ²₃ of his money. In the end, Cole and Natalie had the same amount of money left. Find the amount of money Cole had at first.

	Natalie	Cole	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 Natalie's money left
= 1 - ¹₃
= ²₃

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

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

²₃ of Natalie's money = ¹₃ of Cole's money
²₃ of Natalie's money = ²₆ of Cole's money

Amount that Natalie had at first = 3 u
Amount that Cole had at first = 6 u

Amount that Natalie had less than Cole had at first
= 6 u - 3 u
= 3 u

3 u = 108

1 u = 108 ÷ 3 = 36

Amount that Cole had at first
= 6 u
= 6 x 36
= $216

Answer(s): $216