Yen had some money. She spent 40% on rent and 30% of her remaining money on a vest. She had $294 left.

1. How much did she have at first?
2. If the vest was bought at a 25% discount, what was the original price of the vest?

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

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

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

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

21 u = 294

1 u = 294 ÷ 21 = 14

Amount that Yen had at first
= 50 u
= 50 x 14
= $700

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

Amount that Yen spent on the vest
= 9 u
= 9 x 14
= $126

Discounted price of the vest in percent
= 100% - 25%
= 75%

75% of the price of the vest = 126
1% of the price of the vest = 126 ÷ 75 = 1.68
100% of the price of the vest = 100 x 1.68 = 168

Original price of the vest = $168

Answer(s): (a) $700; (b) $168