Gwen had some money. She spent 25% on a tour and 10% of her remaining money on a jacket. She had $324 left.

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

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

Percent of Gwen's remaining amount left after she spent on the jacket
= 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 = 324

1 u = 324 ÷ 27 = 12

Amount that Gwen had at first
= 40 u
= 40 x 12
= $480

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

Amount that Gwen spent on the jacket
= 3 u
= 3 x 12
= $36

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

75% of the price of the jacket = 36
1% of the price of the jacket = 36 ÷ 75 = 0.48
100% of the price of the jacket = 100 x 0.48 = 48

Original price of the jacket = $48

Answer(s): (a) $480; (b) $48