Shiyun had some money. She spent 20% on books and 30% of her remaining money on a windbreaker. She had $42 left.

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

(a)
Percent of Shiyun's amount left after she spent on books
= 100% - 20%
= 80%

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

Fraction of Shiyun's amount left
= 70% x 80% 
= ⁷⁰₁₀₀ x ⁸⁰₁₀₀
= ¹⁴₂₅

Total amount that Shiyun had = 25 u
Amount that Shiyun had left = 14 u

14 u = 42

1 u = 42 ÷ 14 = 3

Amount that Shiyun had at first
= 25 u
= 25 x 3
= $75

(b)
Fraction of Shiyun's amount spent on the windbreaker
= 30% x 80% 
= ³⁰₁₀₀ x ⁸⁰₁₀₀ 
= ⁶₂₅

Amount that Shiyun spent on the windbreaker
= 6 u
= 6 x 3
= $18

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

75% of the price of the windbreaker = 18
1% of the price of the windbreaker = 18 ÷ 75 = 0.24
100% of the price of the windbreaker = 100 x 0.24 = 24

Original price of the windbreaker = $24

Answer(s): (a) $75; (b) $24