Cathy had some money. She spent 10% on rent and 30% of her remaining money on a dress. She had $126 left.
- How much did she have at first?
- If the dress was bought at a 10% discount, what was the original price of the dress?
(a)
Percent of Cathy's amount left after she spent on rent
= 100% - 10%
= 90%
Percent of Cathy's remaining amount left after she spent on the dress
= 100% - 30%
= 70%
Fraction of Cathy's amount left
= 70% x 90%
=
70100 x
90100=
63100Total amount that Cathy had = 100 u
Amount that Cathy had left = 63 u
63 u = 126
1 u = 126 ÷ 63 = 2
Amount that Cathy had at first
= 100 u
= 100 x 2
= $200
(b)
Fraction of Cathy's amount spent on the dress
= 30% x 90%
=
30100 x
90100 =
27100Amount that Cathy spent on the dress
= 27 u
= 27 x 2
= $54
Discounted price of the dress in percent
= 100% - 10%
= 90%
90% of the price of the dress = 54
1% of the price of the dress = 54 ÷ 90 = 0.6
100% of the price of the dress = 100 x 0.6 = 60
Original price of the dress = $60
Answer(s): (a) $200; (b) $60