Wendy had some money. She spent 40% on a tour and 25% of her remaining money on a vest. She had $117 left.

1. How much did she have at first?
2. If the vest was bought at a 25% discount, what was the original price of the vest?

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

Percent of Wendy's remaining amount left after she spent on the vest
= 100% - 25%
= 75%

Fraction of Wendy's amount left
= 75% x 60% 
= ⁷⁵₁₀₀ x ⁶⁰₁₀₀
= ⁹₂₀

Total amount that Wendy had = 20 u
Amount that Wendy had left = 9 u

9 u = 117

1 u = 117 ÷ 9 = 13

Amount that Wendy had at first
= 20 u
= 20 x 13
= $260

(b)
Fraction of Wendy's amount spent on the vest
= 25% x 60% 
= ²⁵₁₀₀ x ⁶⁰₁₀₀ 
= ³₂₀

Amount that Wendy spent on the vest
= 3 u
= 3 x 13
= $39

Discounted price of the vest in percent
= 100% - 25%
= 75%

75% of the price of the vest = 39
1% of the price of the vest = 39 ÷ 75 = 0.52
100% of the price of the vest = 100 x 0.52 = 52

Original price of the vest = $52

Answer(s): (a) $260; (b) $52