Rachel had some money. She spent 20% on food and 40% of her remaining money on a jumpsuit. She had $36 left.

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

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

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

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

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

12 u = 36

1 u = 36 ÷ 12 = 3

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

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

Amount that Rachel spent on the jumpsuit
= 8 u
= 8 x 3
= $24

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

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

Original price of the jumpsuit = $40

Answer(s): (a) $75; (b) $40