Kylie had some money. She spent 40% on a tour and 20% of her remaining money on a vest. She had $108 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 Kylie's amount left after she spent on a tour
= 100% - 40%
= 60%

Percent of Kylie's remaining amount left after she spent on the vest
= 100% - 20%
= 80%

Fraction of Kylie's amount left
= 80% x 60% 
= ⁸⁰₁₀₀ x ⁶⁰₁₀₀
= ¹²₂₅

Total amount that Kylie had = 25 u
Amount that Kylie had left = 12 u

12 u = 108

1 u = 108 ÷ 12 = 9

Amount that Kylie had at first
= 25 u
= 25 x 9
= $225

(b)
Fraction of Kylie's amount spent on the vest
= 20% x 60% 
= ²⁰₁₀₀ x ⁶⁰₁₀₀ 
= ³₂₅

Amount that Kylie spent on the vest
= 3 u
= 3 x 9
= $27

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

90% of the price of the vest = 27
1% of the price of the vest = 27 ÷ 90 = 0.3
100% of the price of the vest = 100 x 0.3 = 30

Original price of the vest = $30

Answer(s): (a) $225; (b) $30