Hazel had some money. She spent 25% on books and 10% of her remaining money on a skirt. She had $54 left.

1. How much did she have at first?
2. If the skirt was bought at a 25% discount, what was the original price of the skirt?

(a)
Percent of Hazel's amount left after she spent on books
= 100% - 25%
= 75%

Percent of Hazel's remaining amount left after she spent on the skirt
= 100% - 10%
= 90%

Fraction of Hazel's amount left
= 90% x 75% 
= ⁹⁰₁₀₀ x ⁷⁵₁₀₀
= ²⁷₄₀

Total amount that Hazel had = 40 u
Amount that Hazel had left = 27 u

27 u = 54

1 u = 54 ÷ 27 = 2

Amount that Hazel had at first
= 40 u
= 40 x 2
= $80

(b)
Fraction of Hazel's amount spent on the skirt
= 10% x 75% 
= ¹⁰₁₀₀ x ⁷⁵₁₀₀ 
= ³₄₀

Amount that Hazel spent on the skirt
= 3 u
= 3 x 2
= $6

Discounted price of the skirt in percent
= 100% - 25%
= 75%

75% of the price of the skirt = 6
1% of the price of the skirt = 6 ÷ 75 = 0.08
100% of the price of the skirt = 100 x 0.08 = 8

Original price of the skirt = $8

Answer(s): (a) $80; (b) $8