Linda had $1105 less than Vincent. Linda spent ¹₆ of her money and Vincent spent ³₅ of his money. In the end, Vincent and Linda had the same amount of money left. Find the amount of money Vincent had at first.

	Linda	Vincent	Difference
Before	6x2 = 12 u	5x5 = 25 u	13 u
Change	- 1x2 = - 2 u	- 3x5 = - 15 u
After	5x2 = 10 u	2x5 = 10 u

Fraction of Linda's money left
= 1 - ¹₆
= ⁵₆

Fraction of Vincent's money left
= 1 - ³₅
= ²₅

Vincent and Linda had the same amount of money in the end. Make the numerators the same. LCM of 5 and 2 is 10.

⁵₆ of Linda's money = ²₅ of Vincent's money
¹⁰₁₂ of Linda's money = ¹⁰₂₅ of Vincent's money

Amount that Linda had at first = 12 u
Amount that Vincent had at first = 25 u

Amount that Linda had less than Vincent had at first
= 25 u - 12 u
= 13 u

13 u = 1105

1 u = 1105 ÷ 13 = 85

Amount that Vincent had at first
= 25 u
= 25 x 85
= $2125

Answer(s): $2125