Barbara had some money. She spent 10% on food and 30% of her remaining money on a shirt. She had $315 left.
- How much did she have at first?
- If the shirt was bought at a 10% discount, what was the original price of the shirt?
(a)
Percent of Barbara's amount left after she spent on food
= 100% - 10%
= 90%
Percent of Barbara's remaining amount left after she spent on the shirt
= 100% - 30%
= 70%
Fraction of Barbara's amount left
= 70% x 90%
=
70100 x
90100=
63100Total amount that Barbara had = 100 u
Amount that Barbara had left = 63 u
63 u = 315
1 u = 315 ÷ 63 = 5
Amount that Barbara had at first
= 100 u
= 100 x 5
= $500
(b)
Fraction of Barbara's amount spent on the shirt
= 30% x 90%
=
30100 x
90100 =
27100Amount that Barbara spent on the shirt
= 27 u
= 27 x 5
= $135
Discounted price of the shirt in percent
= 100% - 10%
= 90%
90% of the price of the shirt = 135
1% of the price of the shirt = 135 ÷ 90 = 1.5
100% of the price of the shirt = 100 x 1.5 = 150
Original price of the shirt = $150
Answer(s): (a) $500; (b) $150