Emma had some money. She spent 20% on rent and 30% of her remaining money on a vest. She had $84 left.
- How much did she have at first?
- If the vest was bought at a 20% discount, what was the original price of the vest?
(a)
Percent of Emma's amount left after she spent on rent
= 100% - 20%
= 80%
Percent of Emma's remaining amount left after she spent on the vest
= 100% - 30%
= 70%
Fraction of Emma's amount left
= 70% x 80%
=
70100 x
80100=
1425Total amount that Emma had = 25 u
Amount that Emma had left = 14 u
14 u = 84
1 u = 84 ÷ 14 = 6
Amount that Emma had at first
= 25 u
= 25 x 6
= $150
(b)
Fraction of Emma's amount spent on the vest
= 30% x 80%
=
30100 x
80100 =
625Amount that Emma spent on the vest
= 6 u
= 6 x 6
= $36
Discounted price of the vest in percent
= 100% - 20%
= 80%
80% of the price of the vest = 36
1% of the price of the vest = 36 ÷ 80 = 0.45
100% of the price of the vest = 100 x 0.45 = 45
Original price of the vest = $45
Answer(s): (a) $150; (b) $45