Kathy had some money. She spent 20% on food and 30% of her remaining money on a shirt. She had $56 left.

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

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

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

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

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

14 u = 56

1 u = 56 ÷ 14 = 4

Amount that Kathy had at first
= 25 u
= 25 x 4
= $100

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

Amount that Kathy spent on the shirt
= 6 u
= 6 x 4
= $24

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

60% of the price of the shirt = 24
1% of the price of the shirt = 24 ÷ 60 = 0.4
100% of the price of the shirt = 100 x 0.4 = 40

Original price of the shirt = $40

Answer(s): (a) $100; (b) $40