Opal had some money. She spent 40% on a tour and 10% of her remaining money on a windbreaker. She had $405 left.

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

(a)
Percent of Opal's amount left after she spent on a tour
= 100% - 40%
= 60%

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

Fraction of Opal's amount left
= 90% x 60% 
= ⁹⁰₁₀₀ x ⁶⁰₁₀₀
= ²⁷₅₀

Total amount that Opal had = 50 u
Amount that Opal had left = 27 u

27 u = 405

1 u = 405 ÷ 27 = 15

Amount that Opal had at first
= 50 u
= 50 x 15
= $750

(b)
Fraction of Opal's amount spent on the windbreaker
= 10% x 60% 
= ¹⁰₁₀₀ x ⁶⁰₁₀₀ 
= ³₅₀

Amount that Opal spent on the windbreaker
= 3 u
= 3 x 15
= $45

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

60% of the price of the windbreaker = 45
1% of the price of the windbreaker = 45 ÷ 60 = 0.75
100% of the price of the windbreaker = 100 x 0.75 = 75

Original price of the windbreaker = $75

Answer(s): (a) $750; (b) $75