Xuan had some money. She spent 10% on books and 25% of her remaining money on a dress. She had $405 left.

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

(a)
Percent of Xuan's amount left after she spent on books
= 100% - 10%
= 90%

Percent of Xuan's remaining amount left after she spent on the dress
= 100% - 25%
= 75%

Fraction of Xuan's amount left
= 75% x 90% 
= ⁷⁵₁₀₀ x ⁹⁰₁₀₀
= ²⁷₄₀

Total amount that Xuan had = 40 u
Amount that Xuan had left = 27 u

27 u = 405

1 u = 405 ÷ 27 = 15

Amount that Xuan had at first
= 40 u
= 40 x 15
= $600

(b)
Fraction of Xuan's amount spent on the dress
= 25% x 90% 
= ²⁵₁₀₀ x ⁹⁰₁₀₀ 
= ⁹₄₀

Amount that Xuan spent on the dress
= 9 u
= 9 x 15
= $135

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

90% of the price of the dress = 135
1% of the price of the dress = 135 ÷ 90 = 1.5
100% of the price of the dress = 100 x 1.5 = 150

Original price of the dress = $150

Answer(s): (a) $600; (b) $150