Gillian had $1794 less than Vincent. Gillian spent ¹₆ of her money and Vincent spent ⁵₇ of his money. In the end, Vincent and Gillian had the same amount of money left. Find the amount of money Vincent had at first.

	Gillian	Vincent	Difference
Before	6x2 = 12 u	7x5 = 35 u	23 u
Change	- 1x2 = - 2 u	- 5x5 = - 25 u
After	5x2 = 10 u	2x5 = 10 u

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

Fraction of Vincent's money left
= 1 - ⁵₇
= ²₇

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

⁵₆ of Gillian's money = ²₇ of Vincent's money
¹⁰₁₂ of Gillian's money = ¹⁰₃₅ of Vincent's money

Amount that Gillian had at first = 12 u
Amount that Vincent had at first = 35 u

Amount that Gillian had less than Vincent had at first
= 35 u - 12 u
= 23 u

23 u = 1794

1 u = 1794 ÷ 23 = 78

Amount that Vincent had at first
= 35 u
= 35 x 78
= $2730

Answer(s): $2730