Cathy had some money. She spent 40% on books and 20% of her remaining money on a dress. She had $168 left.

1. How much did she have at first?
2. If the dress was bought at a 40% discount, what was the original price of the dress?

(a)
Percent of Cathy's amount left after she spent on books
= 100% - 40%
= 60%

Percent of Cathy's remaining amount left after she spent on the dress
= 100% - 20%
= 80%

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

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

12 u = 168

1 u = 168 ÷ 12 = 14

Amount that Cathy had at first
= 25 u
= 25 x 14
= $350

(b)
Fraction of Cathy's amount spent on the dress
= 20% x 60% 
= ²⁰₁₀₀ x ⁶⁰₁₀₀ 
= ³₂₅

Amount that Cathy spent on the dress
= 3 u
= 3 x 14
= $42

Discounted price of the dress in percent
= 100% - 40%
= 60%

60% of the price of the dress = 42
1% of the price of the dress = 42 ÷ 60 = 0.7
100% of the price of the dress = 100 x 0.7 = 70

Original price of the dress = $70

Answer(s): (a) $350; (b) $70