Esther had some money. She spent 40% on books and 10% of her remaining money on a jumpsuit. She had $378 left.

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

(a)
Percent of Esther's amount left after she spent on books
= 100% - 40%
= 60%

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

Fraction of Esther's amount left
= 90% x 60% 
= ⁹⁰₁₀₀ x ⁶⁰₁₀₀
= ²⁷₅₀

Total amount that Esther had = 50 u
Amount that Esther had left = 27 u

27 u = 378

1 u = 378 ÷ 27 = 14

Amount that Esther had at first
= 50 u
= 50 x 14
= $700

(b)
Fraction of Esther's amount spent on the jumpsuit
= 10% x 60% 
= ¹⁰₁₀₀ x ⁶⁰₁₀₀ 
= ³₅₀

Amount that Esther spent on the jumpsuit
= 3 u
= 3 x 14
= $42

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

60% of the price of the jumpsuit = 42
1% of the price of the jumpsuit = 42 ÷ 60 = 0.7
100% of the price of the jumpsuit = 100 x 0.7 = 70

Original price of the jumpsuit = $70

Answer(s): (a) $700; (b) $70