Olivia had some money. She spent 50% on books and 30% of her remaining money on a skirt. She had $14 left.

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

(a)
Percent of Olivia's amount left after she spent on books
= 100% - 50%
= 50%

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

Fraction of Olivia's amount left
= 70% x 50% 
= ⁷⁰₁₀₀ x ⁵⁰₁₀₀
= ⁷₂₀

Total amount that Olivia had = 20 u
Amount that Olivia had left = 7 u

7 u = 14

1 u = 14 ÷ 7 = 2

Amount that Olivia had at first
= 20 u
= 20 x 2
= $40

(b)
Fraction of Olivia's amount spent on the skirt
= 30% x 50% 
= ³⁰₁₀₀ x ⁵⁰₁₀₀ 
= ³₂₀

Amount that Olivia spent on the skirt
= 3 u
= 3 x 2
= $6

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

60% of the price of the skirt = 6
1% of the price of the skirt = 6 ÷ 60 = 0.1
100% of the price of the skirt = 100 x 0.1 = 10

Original price of the skirt = $10

Answer(s): (a) $40; (b) $10