Hilda had some money. She spent 50% on books and 30% of her remaining money on a blazer. She had $84 left.

1. How much did she have at first?
2. If the blazer was bought at a 10% discount, what was the original price of the blazer?

(a)
Percent of Hilda's amount left after she spent on books
= 100% - 50%
= 50%

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

Fraction of Hilda's amount left
= 70% x 50% 
= ⁷⁰₁₀₀ x ⁵⁰₁₀₀
= ⁷₂₀

Total amount that Hilda had = 20 u
Amount that Hilda had left = 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Amount that Hilda had at first
= 20 u
= 20 x 12
= $240

(b)
Fraction of Hilda's amount spent on the blazer
= 30% x 50% 
= ³⁰₁₀₀ x ⁵⁰₁₀₀ 
= ³₂₀

Amount that Hilda spent on the blazer
= 3 u
= 3 x 12
= $36

Discounted price of the blazer in percent
= 100% - 10%
= 90%

90% of the price of the blazer = 36
1% of the price of the blazer = 36 ÷ 90 = 0.4
100% of the price of the blazer = 100 x 0.4 = 40

Original price of the blazer = $40

Answer(s): (a) $240; (b) $40