Olivia had some money. She spent 20% on a tour and 40% of her remaining money on a jumpsuit. She had $180 left.

1. How much did she have at first?
2. If the jumpsuit was bought at a 20% discount, what was the original price of the jumpsuit?

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

Percent of Olivia's remaining amount left after she spent on the jumpsuit
= 100% - 40%
= 60%

Fraction of Olivia's amount left
= 60% x 80% 
= ⁶⁰₁₀₀ x ⁸⁰₁₀₀
= ¹²₂₅

Total amount that Olivia had = 25 u
Amount that Olivia had left = 12 u

12 u = 180

1 u = 180 ÷ 12 = 15

Amount that Olivia had at first
= 25 u
= 25 x 15
= $375

(b)
Fraction of Olivia's amount spent on the jumpsuit
= 40% x 80% 
= ⁴⁰₁₀₀ x ⁸⁰₁₀₀ 
= ⁸₂₅

Amount that Olivia spent on the jumpsuit
= 8 u
= 8 x 15
= $120

Discounted price of the jumpsuit in percent
= 100% - 20%
= 80%

80% of the price of the jumpsuit = 120
1% of the price of the jumpsuit = 120 ÷ 80 = 1.5
100% of the price of the jumpsuit = 100 x 1.5 = 150

Original price of the jumpsuit = $150

Answer(s): (a) $375; (b) $150