Hazel had some money. She spent 25% on rent and 30% of her remaining money on a shirt. She had $63 left.

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

(a)
Percent of Hazel's amount left after she spent on rent
= 100% - 25%
= 75%

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

Fraction of Hazel's amount left
= 70% x 75% 
= ⁷⁰₁₀₀ x ⁷⁵₁₀₀
= ²¹₄₀

Total amount that Hazel had = 40 u
Amount that Hazel had left = 21 u

21 u = 63

1 u = 63 ÷ 21 = 3

Amount that Hazel had at first
= 40 u
= 40 x 3
= $120

(b)
Fraction of Hazel's amount spent on the shirt
= 30% x 75% 
= ³⁰₁₀₀ x ⁷⁵₁₀₀ 
= ⁹₄₀

Amount that Hazel spent on the shirt
= 9 u
= 9 x 3
= $27

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

90% of the price of the shirt = 27
1% of the price of the shirt = 27 ÷ 90 = 0.3
100% of the price of the shirt = 100 x 0.3 = 30

Original price of the shirt = $30

Answer(s): (a) $120; (b) $30