Olivia had $300 less than Archie. Archie spent 0.6 of his money and Olivia spent 0.3 of her money. In the end, Archie and Olivia had the same amount of money left. Find the amount of money Olivia had at first.

	Olivia	Archie	Difference
Before	20 u	35 u	15 u
Change	- 2 u	- 7 u
After	14 u	14 u

0.6 = ³₅

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

0.3 = ³₁₀

Fraction of Olivia's amount left
= 1 - ³₁₀
= ⁷₁₀

The amount that Archie and Olivia each had in the end is the same. Make the numerators the same. LCM of 2 and 7 is 14.

²₅ of Archie's amount = ⁷₁₀ of Olivia's amount
¹⁴₃₅ of Archie's amount = ¹⁴₂₀ of Olivia's amount

Amount that Olivia had less than Archie
= 35 u - 20 u
= 15 u

15 u = 300

1 u = 300 ÷ 15 = 20

Amount that Olivia had at first
= 20 u
= 20 x 20
= $400

Answer(s): $400