Penelope had $435 less than Bryan. Bryan spent 0.8 of his money and Penelope spent 0.2 of her money. In the end, Bryan and Penelope had the same amount of money left. Find the amount of money Penelope had at first.

	Penelope	Bryan	Difference
Before	5 u	20 u	15 u
Change	- 1 u	- 4 u
After	4 u	4 u

0.8 = ⁴₅

Fraction of Bryan's amount left
= 1 - ⁴₅
= ¹₅

0.2 = ¹₅

Fraction of Penelope's amount left
= 1 - ¹₅
= ⁴₅

The amount that Bryan and Penelope each had in the end is the same. Make the numerators the same. LCM of 1 and 4 is 4.

¹₅ of Bryan's amount = ⁴₅ of Penelope's amount
⁴₂₀ of Bryan's amount = ⁴₅ of Penelope's amount

Amount that Penelope had less than Bryan
= 20 u - 5 u
= 15 u

15 u = 435

1 u = 435 ÷ 15 = 29

Amount that Penelope had at first
= 5 u
= 5 x 29
= $145

Answer(s): $145