Sarah had some money. She spent 40% on books and 20% of her remaining money on a sweater. She had $96 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 Sarah's amount left after she spent on books
= 100% - 40%
= 60%

Percent of Sarah's remaining amount left after she spent on the sweater
= 100% - 20%
= 80%

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

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

12 u = 96

1 u = 96 ÷ 12 = 8

Amount that Sarah had at first
= 25 u
= 25 x 8
= $200

(b)
Fraction of Sarah's amount spent on the sweater
= 20% x 60% 
= ²⁰₁₀₀ x ⁶⁰₁₀₀ 
= ³₂₅

Amount that Sarah spent on the sweater
= 3 u
= 3 x 8
= $24

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

75% of the price of the sweater = 24
1% of the price of the sweater = 24 ÷ 75 = 0.32
100% of the price of the sweater = 100 x 0.32 = 32

Original price of the sweater = $32

Answer(s): (a) $200; (b) $32