Gillian had some money. She spent 10% on food and 25% of her remaining money on a dress. She had $162 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 Gillian's amount left after she spent on food
= 100% - 10%
= 90%

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

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

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

27 u = 162

1 u = 162 ÷ 27 = 6

Amount that Gillian had at first
= 40 u
= 40 x 6
= $240

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

Amount that Gillian spent on the dress
= 9 u
= 9 x 6
= $54

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

90% of the price of the dress = 54
1% of the price of the dress = 54 ÷ 90 = 0.6
100% of the price of the dress = 100 x 0.6 = 60

Original price of the dress = $60

Answer(s): (a) $240; (b) $60