Olivia had some money. She spent 40% on food and 30% of her remaining money on a vest. She had $42 left.

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

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

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

Fraction of Olivia's amount left
= 70% x 60% 
= ⁷⁰₁₀₀ x ⁶⁰₁₀₀
= ²¹₅₀

Total amount that Olivia had = 50 u
Amount that Olivia had left = 21 u

21 u = 42

1 u = 42 ÷ 21 = 2

Amount that Olivia had at first
= 50 u
= 50 x 2
= $100

(b)
Fraction of Olivia's amount spent on the vest
= 30% x 60% 
= ³⁰₁₀₀ x ⁶⁰₁₀₀ 
= ⁹₅₀

Amount that Olivia spent on the vest
= 9 u
= 9 x 2
= $18

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

90% of the price of the vest = 18
1% of the price of the vest = 18 ÷ 90 = 0.2
100% of the price of the vest = 100 x 0.2 = 20

Original price of the vest = $20

Answer(s): (a) $100; (b) $20