Jen had $637 less than Vincent. Jen spent ¹₅ of her money and Vincent spent ⁴₇ of his money. In the end, Vincent and Jen had the same amount of money left. Find the amount of money Vincent had at first.

	Jen	Vincent	Difference
Before	5x3 = 15 u	7x4 = 28 u	13 u
Change	- 1x3 = - 3 u	- 4x4 = - 16 u
After	4x3 = 12 u	3x4 = 12 u

Fraction of Jen's money left
= 1 - ¹₅
= ⁴₅

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

Vincent and Jen had the same amount of money in the end. Make the numerators the same. LCM of 4 and 3 is 12.

⁴₅ of Jen's money = ³₇ of Vincent's money
¹²₁₅ of Jen's money = ¹²₂₈ of Vincent's money

Amount that Jen had at first = 15 u
Amount that Vincent had at first = 28 u

Amount that Jen had less than Vincent had at first
= 28 u - 15 u
= 13 u

13 u = 637

1 u = 637 ÷ 13 = 49

Amount that Vincent had at first
= 28 u
= 28 x 49
= $1372

Answer(s): $1372