Ivory had some money. She spent 10% on books and 30% of her remaining money on a shirt. She had $567 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 Ivory's amount left after she spent on books
= 100% - 10%
= 90%

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

Fraction of Ivory's amount left
= 70% x 90% 
= ⁷⁰₁₀₀ x ⁹⁰₁₀₀
= ⁶³₁₀₀

Total amount that Ivory had = 100 u
Amount that Ivory had left = 63 u

63 u = 567

1 u = 567 ÷ 63 = 9

Amount that Ivory had at first
= 100 u
= 100 x 9
= $900

(b)
Fraction of Ivory's amount spent on the shirt
= 30% x 90% 
= ³⁰₁₀₀ x ⁹⁰₁₀₀ 
= ²⁷₁₀₀

Amount that Ivory spent on the shirt
= 27 u
= 27 x 9
= $243

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

60% of the price of the shirt = 243
1% of the price of the shirt = 243 ÷ 60 = 4.05
100% of the price of the shirt = 100 x 4.05 = 405

Original price of the shirt = $405

Answer(s): (a) $900; (b) $405