Victoria had some money. She spent 40% on food and 10% of her remaining money on a skirt. She had $405 left.

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

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

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

Fraction of Victoria's amount left
= 90% x 60% 
= ⁹⁰₁₀₀ x ⁶⁰₁₀₀
= ²⁷₅₀

Total amount that Victoria had = 50 u
Amount that Victoria had left = 27 u

27 u = 405

1 u = 405 ÷ 27 = 15

Amount that Victoria had at first
= 50 u
= 50 x 15
= $750

(b)
Fraction of Victoria's amount spent on the skirt
= 10% x 60% 
= ¹⁰₁₀₀ x ⁶⁰₁₀₀ 
= ³₅₀

Amount that Victoria spent on the skirt
= 3 u
= 3 x 15
= $45

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

75% of the price of the skirt = 45
1% of the price of the skirt = 45 ÷ 75 = 0.6
100% of the price of the skirt = 100 x 0.6 = 60

Original price of the skirt = $60

Answer(s): (a) $750; (b) $60