SOLUTION: A store owner bought an item for $40. He marked it to make a 30% profit. The item wouldn�t sell, so he sale priced at a certain discount rate, wanting to make a profit of 10.5 %,

Question 241960: A store owner bought an item for $40. He marked it to make a 30% profit. The
item wouldn�t sell, so he sale priced at a certain discount rate, wanting to make a profit of 10.5 %, based on the original cost. Determine the discount rate as a
percent.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
cost is equal to 40.
original price is equal to 40 + .3*40 = 52
sale price = 40 + .105*40 = 44.20
original price minus sale price = 52 - 44.2 = 7.8
discount percent = discount divided by original price = 7.8/52 = .15 * 100% = 15%

in formula form, this would be shown as follows:

c = cost
p = original price
s = sale price
d = discount off of original price
r = discount rate off of original price
r% = r * 100%

p = c + .3*c
s = c + .105*c
d = p - s
r = d/p
r% = r * 100%

put into numbers:

c = 40
p = 40 + .3*40 = 40 + 12 = 52
s = c + .105*c = 40 + 4.2 = 44.2
d = p - s = 52 - 44.2 = 7.8
r = d/p = 7.8/52 = .15
r% = .15 * 100% = 15%

he buys it at 40.
he puts it on sale at 52.
he discounts it 15% from 52
he sells it at 44.2 and gets a 10.5% profit on the original cost of 40.

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