Fiona had some money. She spent 10% on books and 25% 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 25% discount, what was the original price of the sweater?
(a)
Percent of Fiona's amount left after she spent on books
= 100% - 10%
= 90%
Percent of Fiona's remaining amount left after she spent on the sweater
= 100% - 25%
= 75%
Fraction of Fiona's amount left
= 75% x 90%
=
75100 x
90100=
2740Total amount that Fiona had = 40 u
Amount that Fiona had left = 27 u
27 u = 81
1 u = 81 ÷ 27 = 3
Amount that Fiona had at first
= 40 u
= 40 x 3
= $120
(b)
Fraction of Fiona's amount spent on the sweater
= 25% x 90%
=
25100 x
90100 =
940Amount that Fiona spent on the sweater
= 9 u
= 9 x 3
= $27
Discounted price of the sweater in percent
= 100% - 25%
= 75%
75% of the price of the sweater = 27
1% of the price of the sweater = 27 ÷ 75 = 0.36
100% of the price of the sweater = 100 x 0.36 = 36
Original price of the sweater = $36
Answer(s): (a) $120; (b) $36