Opal had some money. She spent 40% on food and 30% of her remaining money on a sweater. She had $147 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 Opal's amount left after she spent on food
= 100% - 40%
= 60%
Percent of Opal's remaining amount left after she spent on the sweater
= 100% - 30%
= 70%
Fraction of Opal's amount left
= 70% x 60%
=
70100 x
60100=
2150Total amount that Opal had = 50 u
Amount that Opal had left = 21 u
21 u = 147
1 u = 147 ÷ 21 = 7
Amount that Opal had at first
= 50 u
= 50 x 7
= $350
(b)
Fraction of Opal's amount spent on the sweater
= 30% x 60%
=
30100 x
60100 =
950Amount that Opal spent on the sweater
= 9 u
= 9 x 7
= $63
Discounted price of the sweater in percent
= 100% - 25%
= 75%
75% of the price of the sweater = 63
1% of the price of the sweater = 63 ÷ 75 = 0.84
100% of the price of the sweater = 100 x 0.84 = 84
Original price of the sweater = $84
Answer(s): (a) $350; (b) $84