Sarah had some money. She spent 20% on books and 30% of her remaining money on a blazer. She had $70 left.

1. How much did she have at first?
2. If the blazer was bought at a 25% discount, what was the original price of the blazer?

(a)
Percent of Sarah's amount left after she spent on books
= 100% - 20%
= 80%

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

Fraction of Sarah's amount left
= 70% x 80% 
= ⁷⁰₁₀₀ x ⁸⁰₁₀₀
= ¹⁴₂₅

Total amount that Sarah had = 25 u
Amount that Sarah had left = 14 u

14 u = 70

1 u = 70 ÷ 14 = 5

Amount that Sarah had at first
= 25 u
= 25 x 5
= $125

(b)
Fraction of Sarah's amount spent on the blazer
= 30% x 80% 
= ³⁰₁₀₀ x ⁸⁰₁₀₀ 
= ⁶₂₅

Amount that Sarah spent on the blazer
= 6 u
= 6 x 5
= $30

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

75% of the price of the blazer = 30
1% of the price of the blazer = 30 ÷ 75 = 0.4
100% of the price of the blazer = 100 x 0.4 = 40

Original price of the blazer = $40

Answer(s): (a) $125; (b) $40