Wendy had some money. She spent 10% on books and 25% of her remaining money on a sweater. She had $378 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 Wendy's amount left after she spent on books
= 100% - 10%
= 90%

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

Fraction of Wendy's amount left
= 75% x 90% 
= ⁷⁵₁₀₀ x ⁹⁰₁₀₀
= ²⁷₄₀

Total amount that Wendy had = 40 u
Amount that Wendy had left = 27 u

27 u = 378

1 u = 378 ÷ 27 = 14

Amount that Wendy had at first
= 40 u
= 40 x 14
= $560

(b)
Fraction of Wendy's amount spent on the sweater
= 25% x 90% 
= ²⁵₁₀₀ x ⁹⁰₁₀₀ 
= ⁹₄₀

Amount that Wendy spent on the sweater
= 9 u
= 9 x 14
= $126

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

70% of the price of the sweater = 126
1% of the price of the sweater = 126 ÷ 70 = 1.8
100% of the price of the sweater = 100 x 1.8 = 180

Original price of the sweater = $180

Answer(s): (a) $560; (b) $180