Jade had some money. She spent 25% on rent and 30% of her remaining money on a sweater. She had $147 left.

1. How much did she have at first?
2. If the sweater was bought at a 40% discount, what was the original price of the sweater?

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

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

Fraction of Jade's amount left
= 70% x 75% 
= ⁷⁰₁₀₀ x ⁷⁵₁₀₀
= ²¹₄₀

Total amount that Jade had = 40 u
Amount that Jade had left = 21 u

21 u = 147

1 u = 147 ÷ 21 = 7

Amount that Jade had at first
= 40 u
= 40 x 7
= $280

(b)
Fraction of Jade's amount spent on the sweater
= 30% x 75% 
= ³⁰₁₀₀ x ⁷⁵₁₀₀ 
= ⁹₄₀

Amount that Jade spent on the sweater
= 9 u
= 9 x 7
= $63

Discounted price of the sweater in percent
= 100% - 40%
= 60%

60% of the price of the sweater = 63
1% of the price of the sweater = 63 ÷ 60 = 1.05
100% of the price of the sweater = 100 x 1.05 = 105

Original price of the sweater = $105

Answer(s): (a) $280; (b) $105