Lucy had some money. She spent 20% on food and 30% of her remaining money on a sweater. She had $210 left.
- How much did she have at first?
- If the sweater was bought at a 25% discount, what was the original price of the sweater?
(a)
Percent of Lucy's amount left after she spent on food
= 100% - 20%
= 80%
Percent of Lucy's remaining amount left after she spent on the sweater
= 100% - 30%
= 70%
Fraction of Lucy's amount left
= 70% x 80%
=
70100 x
80100=
1425Total amount that Lucy had = 25 u
Amount that Lucy had left = 14 u
14 u = 210
1 u = 210 ÷ 14 = 15
Amount that Lucy had at first
= 25 u
= 25 x 15
= $375
(b)
Fraction of Lucy's amount spent on the sweater
= 30% x 80%
=
30100 x
80100 =
625Amount that Lucy spent on the sweater
= 6 u
= 6 x 15
= $90
Discounted price of the sweater in percent
= 100% - 25%
= 75%
75% of the price of the sweater = 90
1% of the price of the sweater = 90 ÷ 75 = 1.2
100% of the price of the sweater = 100 x 1.2 = 120
Original price of the sweater = $120
Answer(s): (a) $375; (b) $120