Victoria had some money. She spent 20% on a tour and 40% of her remaining money on a sweater. She had $48 left.

1. How much did she have at first?
2. If the sweater was bought at a 20% discount, what was the original price of the sweater?

(a)
Percent of Victoria's amount left after she spent on a tour
= 100% - 20%
= 80%

Percent of Victoria's remaining amount left after she spent on the sweater
= 100% - 40%
= 60%

Fraction of Victoria's amount left
= 60% x 80% 
= ⁶⁰₁₀₀ x ⁸⁰₁₀₀
= ¹²₂₅

Total amount that Victoria had = 25 u
Amount that Victoria had left = 12 u

12 u = 48

1 u = 48 ÷ 12 = 4

Amount that Victoria had at first
= 25 u
= 25 x 4
= $100

(b)
Fraction of Victoria's amount spent on the sweater
= 40% x 80% 
= ⁴⁰₁₀₀ x ⁸⁰₁₀₀ 
= ⁸₂₅

Amount that Victoria spent on the sweater
= 8 u
= 8 x 4
= $32

Discounted price of the sweater in percent
= 100% - 20%
= 80%

80% of the price of the sweater = 32
1% of the price of the sweater = 32 ÷ 80 = 0.4
100% of the price of the sweater = 100 x 0.4 = 40

Original price of the sweater = $40

Answer(s): (a) $100; (b) $40