Kimberly had some money. She spent 40% on food and 30% of her remaining money on a sweater. She had $105 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 Kimberly's amount left after she spent on food
= 100% - 40%
= 60%

Percent of Kimberly's remaining amount left after she spent on the sweater
= 100% - 30%
= 70%

Fraction of Kimberly's amount left
= 70% x 60% 
= ⁷⁰₁₀₀ x ⁶⁰₁₀₀
= ²¹₅₀

Total amount that Kimberly had = 50 u
Amount that Kimberly had left = 21 u

21 u = 105

1 u = 105 ÷ 21 = 5

Amount that Kimberly had at first
= 50 u
= 50 x 5
= $250

(b)
Fraction of Kimberly's amount spent on the sweater
= 30% x 60% 
= ³⁰₁₀₀ x ⁶⁰₁₀₀ 
= ⁹₅₀

Amount that Kimberly spent on the sweater
= 9 u
= 9 x 5
= $45

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

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

Original price of the sweater = $60

Answer(s): (a) $250; (b) $60