Gabby had some money. She spent 20% on rent and 40% of her remaining money on a sweater. She had $84 left.
- How much did she have at first?
- If the sweater was bought at a 30% discount, what was the original price of the sweater?
(a)
Percent of Gabby's amount left after she spent on rent
= 100% - 20%
= 80%
Percent of Gabby's remaining amount left after she spent on the sweater
= 100% - 40%
= 60%
Fraction of Gabby's amount left
= 60% x 80%
=
60100 x
80100=
1225Total amount that Gabby had = 25 u
Amount that Gabby had left = 12 u
12 u = 84
1 u = 84 ÷ 12 = 7
Amount that Gabby had at first
= 25 u
= 25 x 7
= $175
(b)
Fraction of Gabby's amount spent on the sweater
= 40% x 80%
=
40100 x
80100 =
825Amount that Gabby spent on the sweater
= 8 u
= 8 x 7
= $56
Discounted price of the sweater in percent
= 100% - 30%
= 70%
70% of the price of the sweater = 56
1% of the price of the sweater = 56 ÷ 70 = 0.8
100% of the price of the sweater = 100 x 0.8 = 80
Original price of the sweater = $80
Answer(s): (a) $175; (b) $80