Gabby had some money. She spent 25% on a tour and 10% of her remaining money on a sweater. She had $54 left.

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

(a)
Percent of Gabby's amount left after she spent on a tour
= 100% - 25%
= 75%

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

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

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

27 u = 54

1 u = 54 ÷ 27 = 2

Amount that Gabby had at first
= 40 u
= 40 x 2
= $80

(b)
Fraction of Gabby's amount spent on the sweater
= 10% x 75% 
= ¹⁰₁₀₀ x ⁷⁵₁₀₀ 
= ³₄₀

Amount that Gabby spent on the sweater
= 3 u
= 3 x 2
= $6

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

75% of the price of the sweater = 6
1% of the price of the sweater = 6 ÷ 75 = 0.08
100% of the price of the sweater = 100 x 0.08 = 8

Original price of the sweater = $8

Answer(s): (a) $80; (b) $8