Xylia had some money. She spent 20% on rent and 10% of her remaining money on a dress. She had $126 left.

1. How much did she have at first?
2. If the dress was bought at a 30% discount, what was the original price of the dress?

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

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

Fraction of Xylia's amount left
= 90% x 80% 
= ⁹⁰₁₀₀ x ⁸⁰₁₀₀
= ¹⁸₂₅

Total amount that Xylia had = 25 u
Amount that Xylia had left = 18 u

18 u = 126

1 u = 126 ÷ 18 = 7

Amount that Xylia had at first
= 25 u
= 25 x 7
= $175

(b)
Fraction of Xylia's amount spent on the dress
= 10% x 80% 
= ¹⁰₁₀₀ x ⁸⁰₁₀₀ 
= ²₂₅

Amount that Xylia spent on the dress
= 2 u
= 2 x 7
= $14

Discounted price of the dress in percent
= 100% - 30%
= 70%

70% of the price of the dress = 14
1% of the price of the dress = 14 ÷ 70 = 0.2
100% of the price of the dress = 100 x 0.2 = 20

Original price of the dress = $20

Answer(s): (a) $175; (b) $20