Nicole had some money. She spent 40% on books and 10% of her remaining money on a coat. She had $216 left.

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

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

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

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

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

27 u = 216

1 u = 216 ÷ 27 = 8

Amount that Nicole had at first
= 50 u
= 50 x 8
= $400

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

Amount that Nicole spent on the coat
= 3 u
= 3 x 8
= $24

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

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

Original price of the coat = $40

Answer(s): (a) $400; (b) $40