Sarah had some money. She spent 10% on food and 25% of her remaining money on a coat. She had $135 left.

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

(a)
Percent of Sarah's amount left after she spent on food
= 100% - 10%
= 90%

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

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

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

27 u = 135

1 u = 135 ÷ 27 = 5

Amount that Sarah had at first
= 40 u
= 40 x 5
= $200

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

Amount that Sarah spent on the coat
= 9 u
= 9 x 5
= $45

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

75% of the price of the coat = 45
1% of the price of the coat = 45 ÷ 75 = 0.6
100% of the price of the coat = 100 x 0.6 = 60

Original price of the coat = $60

Answer(s): (a) $200; (b) $60