Fanny had some money. She spent 40% on a tour and 30% of her remaining money on a sweater. She had $273 left.

1. How much did she have at first?
2. If the sweater was bought at a 10% discount, what was the original price of the sweater?

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

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

Fraction of Fanny's amount left
= 70% x 60% 
= ⁷⁰₁₀₀ x ⁶⁰₁₀₀
= ²¹₅₀

Total amount that Fanny had = 50 u
Amount that Fanny had left = 21 u

21 u = 273

1 u = 273 ÷ 21 = 13

Amount that Fanny had at first
= 50 u
= 50 x 13
= $650

(b)
Fraction of Fanny's amount spent on the sweater
= 30% x 60% 
= ³⁰₁₀₀ x ⁶⁰₁₀₀ 
= ⁹₅₀

Amount that Fanny spent on the sweater
= 9 u
= 9 x 13
= $117

Discounted price of the sweater in percent
= 100% - 10%
= 90%

90% of the price of the sweater = 117
1% of the price of the sweater = 117 ÷ 90 = 1.3
100% of the price of the sweater = 100 x 1.3 = 130

Original price of the sweater = $130

Answer(s): (a) $650; (b) $130