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

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

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

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

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

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

27 u = 54

1 u = 54 ÷ 27 = 2

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

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

Amount that Gwen spent on the blouse
= 3 u
= 3 x 2
= $6

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

60% of the price of the blouse = 6
1% of the price of the blouse = 6 ÷ 60 = 0.1
100% of the price of the blouse = 100 x 0.1 = 10

Original price of the blouse = $10

Answer(s): (a) $80; (b) $10