Erika had some money. She spent 20% on books and 30% of her remaining money on a vest. She had $56 left.

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

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

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

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

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

14 u = 56

1 u = 56 ÷ 14 = 4

Amount that Erika had at first
= 25 u
= 25 x 4
= $100

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

Amount that Erika spent on the vest
= 6 u
= 6 x 4
= $24

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

60% of the price of the vest = 24
1% of the price of the vest = 24 ÷ 60 = 0.4
100% of the price of the vest = 100 x 0.4 = 40

Original price of the vest = $40

Answer(s): (a) $100; (b) $40