Sarah had $450 less than Vincent. Vincent spent 0.9 of his money and Sarah spent 0.4 of her money. In the end, Vincent and Sarah had the same amount of money left. Find the amount of money Sarah had at first.

	Sarah	Vincent	Difference
Before	5 u	30 u	25 u
Change	- 1 u	- 3 u
After	3 u	3 u

0.9 = ⁹₁₀

Fraction of Vincent's amount left
= 1 - ⁹₁₀
= ¹₁₀

0.4 = ²₅

Fraction of Sarah's amount left
= 1 - ²₅
= ³₅

The amount that Vincent and Sarah each had in the end is the same. Make the numerators the same. LCM of 1 and 3 is 3.

¹₁₀ of Vincent's amount = ³₅ of Sarah's amount
³₃₀ of Vincent's amount = ³₅ of Sarah's amount

Amount that Sarah had less than Vincent
= 30 u - 5 u
= 25 u

25 u = 450

1 u = 450 ÷ 25 = 18

Amount that Sarah had at first
= 5 u
= 5 x 18
= $90

Answer(s): $90