Tina had some money. She spent 30% on rent and 25% 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 30% discount, what was the original price of the sweater?

(a)
Percent of Tina's amount left after she spent on rent
= 100% - 30%
= 70%

Percent of Tina's remaining amount left after she spent on the sweater
= 100% - 25%
= 75%

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

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

21 u = 147

1 u = 147 ÷ 21 = 7

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

(b)
Fraction of Tina's amount spent on the sweater
= 25% x 70% 
= ²⁵₁₀₀ x ⁷⁰₁₀₀ 
= ⁷₄₀

Amount that Tina spent on the sweater
= 7 u
= 7 x 7
= $49

Discounted price of the sweater in percent
= 100% - 30%
= 70%

70% of the price of the sweater = 49
1% of the price of the sweater = 49 ÷ 70 = 0.7
100% of the price of the sweater = 100 x 0.7 = 70

Original price of the sweater = $70

Answer(s): (a) $280; (b) $70