Diana had some money. She spent 40% on books and 25% of her remaining money on a dress. She had $72 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 Diana's amount left after she spent on books
= 100% - 40%
= 60%

Percent of Diana's remaining amount left after she spent on the dress
= 100% - 25%
= 75%

Fraction of Diana's amount left
= 75% x 60% 
= ⁷⁵₁₀₀ x ⁶⁰₁₀₀
= ⁹₂₀

Total amount that Diana had = 20 u
Amount that Diana had left = 9 u

9 u = 72

1 u = 72 ÷ 9 = 8

Amount that Diana had at first
= 20 u
= 20 x 8
= $160

(b)
Fraction of Diana's amount spent on the dress
= 25% x 60% 
= ²⁵₁₀₀ x ⁶⁰₁₀₀ 
= ³₂₀

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

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

60% of the price of the dress = 24
1% of the price of the dress = 24 ÷ 60 = 0.4
100% of the price of the dress = 100 x 0.4 = 40

Original price of the dress = $40

Answer(s): (a) $160; (b) $40