Fiona had some money. She spent 20% on a tour and 40% of her remaining money on a dress. She had $36 left.

1. How much did she have at first?
2. If the dress was bought at a 20% discount, what was the original price of the dress?

(a)
Percent of Fiona's amount left after she spent on a tour
= 100% - 20%
= 80%

Percent of Fiona's remaining amount left after she spent on the dress
= 100% - 40%
= 60%

Fraction of Fiona's amount left
= 60% x 80% 
= ⁶⁰₁₀₀ x ⁸⁰₁₀₀
= ¹²₂₅

Total amount that Fiona had = 25 u
Amount that Fiona had left = 12 u

12 u = 36

1 u = 36 ÷ 12 = 3

Amount that Fiona had at first
= 25 u
= 25 x 3
= $75

(b)
Fraction of Fiona's amount spent on the dress
= 40% x 80% 
= ⁴⁰₁₀₀ x ⁸⁰₁₀₀ 
= ⁸₂₅

Amount that Fiona spent on the dress
= 8 u
= 8 x 3
= $24

Discounted price of the dress in percent
= 100% - 20%
= 80%

80% of the price of the dress = 24
1% of the price of the dress = 24 ÷ 80 = 0.3
100% of the price of the dress = 100 x 0.3 = 30

Original price of the dress = $30

Answer(s): (a) $75; (b) $30