Diana had some money. She spent 40% on food and 30% of her remaining money on a jacket. She had $189 left.

1. How much did she have at first?
2. If the jacket was bought at a 40% discount, what was the original price of the jacket?

(a)
Percent of Diana's amount left after she spent on food
= 100% - 40%
= 60%

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

Fraction of Diana's amount left
= 70% x 60% 
= ⁷⁰₁₀₀ x ⁶⁰₁₀₀
= ²¹₅₀

Total amount that Diana had = 50 u
Amount that Diana had left = 21 u

21 u = 189

1 u = 189 ÷ 21 = 9

Amount that Diana had at first
= 50 u
= 50 x 9
= $450

(b)
Fraction of Diana's amount spent on the jacket
= 30% x 60% 
= ³⁰₁₀₀ x ⁶⁰₁₀₀ 
= ⁹₅₀

Amount that Diana spent on the jacket
= 9 u
= 9 x 9
= $81

Discounted price of the jacket in percent
= 100% - 40%
= 60%

60% of the price of the jacket = 81
1% of the price of the jacket = 81 ÷ 60 = 1.35
100% of the price of the jacket = 100 x 1.35 = 135

Original price of the jacket = $135

Answer(s): (a) $450; (b) $135