Vanessa had some money. She spent 10% on books and 30% of her remaining money on a coat. She had $819 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 Vanessa's amount left after she spent on books
= 100% - 10%
= 90%

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

Fraction of Vanessa's amount left
= 70% x 90% 
= ⁷⁰₁₀₀ x ⁹⁰₁₀₀
= ⁶³₁₀₀

Total amount that Vanessa had = 100 u
Amount that Vanessa had left = 63 u

63 u = 819

1 u = 819 ÷ 63 = 13

Amount that Vanessa had at first
= 100 u
= 100 x 13
= $1300

(b)
Fraction of Vanessa's amount spent on the coat
= 30% x 90% 
= ³⁰₁₀₀ x ⁹⁰₁₀₀ 
= ²⁷₁₀₀

Amount that Vanessa spent on the coat
= 27 u
= 27 x 13
= $351

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

60% of the price of the coat = 351
1% of the price of the coat = 351 ÷ 60 = 5.85
100% of the price of the coat = 100 x 5.85 = 585

Original price of the coat = $585

Answer(s): (a) $1300; (b) $585