Xuan had some money. She spent 30% on a tour and 10% of her remaining money on a sweater. She had $756 left.

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

(a)
Percent of Xuan's amount left after she spent on a tour
= 100% - 30%
= 70%

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

Fraction of Xuan's amount left
= 90% x 70% 
= ⁹⁰₁₀₀ x ⁷⁰₁₀₀
= ⁶³₁₀₀

Total amount that Xuan had = 100 u
Amount that Xuan had left = 63 u

63 u = 756

1 u = 756 ÷ 63 = 12

Amount that Xuan had at first
= 100 u
= 100 x 12
= $1200

(b)
Fraction of Xuan's amount spent on the sweater
= 10% x 70% 
= ¹⁰₁₀₀ x ⁷⁰₁₀₀ 
= ⁷₁₀₀

Amount that Xuan spent on the sweater
= 7 u
= 7 x 12
= $84

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

60% of the price of the sweater = 84
1% of the price of the sweater = 84 ÷ 60 = 1.4
100% of the price of the sweater = 100 x 1.4 = 140

Original price of the sweater = $140

Answer(s): (a) $1200; (b) $140