Roshel had some money. She spent 30% on food and 10% of her remaining money on a jumpsuit. She had $315 left.

1. How much did she have at first?
2. If the jumpsuit was bought at a 30% discount, what was the original price of the jumpsuit?

(a)
Percent of Roshel's amount left after she spent on food
= 100% - 30%
= 70%

Percent of Roshel's remaining amount left after she spent on the jumpsuit
= 100% - 10%
= 90%

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

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

63 u = 315

1 u = 315 ÷ 63 = 5

Amount that Roshel had at first
= 100 u
= 100 x 5
= $500

(b)
Fraction of Roshel's amount spent on the jumpsuit
= 10% x 70% 
= ¹⁰₁₀₀ x ⁷⁰₁₀₀ 
= ⁷₁₀₀

Amount that Roshel spent on the jumpsuit
= 7 u
= 7 x 5
= $35

Discounted price of the jumpsuit in percent
= 100% - 30%
= 70%

70% of the price of the jumpsuit = 35
1% of the price of the jumpsuit = 35 ÷ 70 = 0.5
100% of the price of the jumpsuit = 100 x 0.5 = 50

Original price of the jumpsuit = $50

Answer(s): (a) $500; (b) $50