Pamela had $595 less than Vincent. Pamela spent ¹₅ of her money and Vincent spent ²₃ of his money. In the end, Vincent and Pamela had the same amount of money left. Find the amount of money Vincent had at first.

	Pamela	Vincent	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 Pamela's money left
= 1 - ¹₅
= ⁴₅

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

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

⁴₅ of Pamela's money = ¹₃ of Vincent's money
⁴₅ of Pamela's money = ⁴₁₂ of Vincent's money

Amount that Pamela had at first = 5 u
Amount that Vincent had at first = 12 u

Amount that Pamela had less than Vincent had at first
= 12 u - 5 u
= 7 u

7 u = 595

1 u = 595 ÷ 7 = 85

Amount that Vincent had at first
= 12 u
= 12 x 85
= $1020

Answer(s): $1020