Dana had some money. She spent 40% on food and 10% of her remaining money on a sweater. She had $81 left.
- How much did she have at first?
- If the sweater was bought at a 10% discount, what was the original price of the sweater?
(a)
Percent of Dana's amount left after she spent on food
= 100% - 40%
= 60%
Percent of Dana's remaining amount left after she spent on the sweater
= 100% - 10%
= 90%
Fraction of Dana's amount left
= 90% x 60%
=
90100 x
60100=
2750Total amount that Dana had = 50 u
Amount that Dana had left = 27 u
27 u = 81
1 u = 81 ÷ 27 = 3
Amount that Dana had at first
= 50 u
= 50 x 3
= $150
(b)
Fraction of Dana's amount spent on the sweater
= 10% x 60%
=
10100 x
60100 =
350Amount that Dana spent on the sweater
= 3 u
= 3 x 3
= $9
Discounted price of the sweater in percent
= 100% - 10%
= 90%
90% of the price of the sweater = 9
1% of the price of the sweater = 9 ÷ 90 = 0.1
100% of the price of the sweater = 100 x 0.1 = 10
Original price of the sweater = $10
Answer(s): (a) $150; (b) $10