Hilda had some money. She spent 10% on a tour and 30% of her remaining money on a dress. She had $945 left.

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

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

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

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

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

63 u = 945

1 u = 945 ÷ 63 = 15

Amount that Hilda had at first
= 100 u
= 100 x 15
= $1500

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

Amount that Hilda spent on the dress
= 27 u
= 27 x 15
= $405

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

75% of the price of the dress = 405
1% of the price of the dress = 405 ÷ 75 = 5.4
100% of the price of the dress = 100 x 5.4 = 540

Original price of the dress = $540

Answer(s): (a) $1500; (b) $540