Gabby had $845 less than Luis. Gabby spent ¹₆ of her money and Luis spent ³₅ of his money. In the end, Luis and Gabby had the same amount of money left. Find the amount of money Luis had at first.

	Gabby	Luis	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 Gabby's money left
= 1 - ¹₆
= ⁵₆

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

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

⁵₆ of Gabby's money = ²₅ of Luis's money
¹⁰₁₂ of Gabby's money = ¹⁰₂₅ of Luis's money

Amount that Gabby had at first = 12 u
Amount that Luis had at first = 25 u

Amount that Gabby had less than Luis had at first
= 25 u - 12 u
= 13 u

13 u = 845

1 u = 845 ÷ 13 = 65

Amount that Luis had at first
= 25 u
= 25 x 65
= $1625

Answer(s): $1625