Elyse had some money. She spent 40% on rent and 25% of her remaining money on a sweater. She had $108 left.

1. How much did she have at first?
2. If the sweater was bought at a 20% discount, what was the original price of the sweater?

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

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

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

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

9 u = 108

1 u = 108 ÷ 9 = 12

Amount that Elyse had at first
= 20 u
= 20 x 12
= $240

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

Amount that Elyse spent on the sweater
= 3 u
= 3 x 12
= $36

Discounted price of the sweater in percent
= 100% - 20%
= 80%

80% of the price of the sweater = 36
1% of the price of the sweater = 36 ÷ 80 = 0.45
100% of the price of the sweater = 100 x 0.45 = 45

Original price of the sweater = $45

Answer(s): (a) $240; (b) $45