Kathy had some money. She spent 25% on a tour and 30% of her remaining money on a windbreaker. She had $63 left.

1. How much did she have at first?
2. If the windbreaker was bought at a 10% discount, what was the original price of the windbreaker?

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

Percent of Kathy's remaining amount left after she spent on the windbreaker
= 100% - 30%
= 70%

Fraction of Kathy's amount left
= 70% x 75% 
= ⁷⁰₁₀₀ x ⁷⁵₁₀₀
= ²¹₄₀

Total amount that Kathy had = 40 u
Amount that Kathy had left = 21 u

21 u = 63

1 u = 63 ÷ 21 = 3

Amount that Kathy had at first
= 40 u
= 40 x 3
= $120

(b)
Fraction of Kathy's amount spent on the windbreaker
= 30% x 75% 
= ³⁰₁₀₀ x ⁷⁵₁₀₀ 
= ⁹₄₀

Amount that Kathy spent on the windbreaker
= 9 u
= 9 x 3
= $27

Discounted price of the windbreaker in percent
= 100% - 10%
= 90%

90% of the price of the windbreaker = 27
1% of the price of the windbreaker = 27 ÷ 90 = 0.3
100% of the price of the windbreaker = 100 x 0.3 = 30

Original price of the windbreaker = $30

Answer(s): (a) $120; (b) $30