Xandra had some money. She spent 25% on a tour and 30% of her remaining money on a shirt. She had $105 left.

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

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

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

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

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

21 u = 105

1 u = 105 ÷ 21 = 5

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

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

Amount that Xandra spent on the shirt
= 9 u
= 9 x 5
= $45

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

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

Original price of the shirt = $60

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