Question 992436: write an equation and solve.
A clothing retailer marks up his merchandise at a rate of 150% so that he can regularly offer a 25% off sale. If the retail price of a sweater is $60, determine the retailer's cost and the sale price.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! r = retail price
c = cost
s = sale price
m = markup rate = 150% / 100 = 1.5
d = discount rate = 25% / 100 = .25
the retail price is equal to the cost plus the markup rate * the cost.
equation is:
r = c + m * c
since m = 1.5, then:
r = c + 1.5 * c
the sale price is equal to the retail price minus the discount rate * the retail price.
equation is:
s = r - d * r
since d = .25, then:
s = r - .25 * r
the two equations are:
r = c + 1.5 * c
s = r - .25 * r
you are given that r is equal to 60.
the equations become:
60 = c + 1.5 * c
s = 60 - .25 * 60
the second equation can be solved as is:
you get:
s = 60 - .25 * 60 which becomes:
s = 60 - 15 which becomes:
s = 45.
the sale price of the sweater is 45 dollars.
the first equation requires a little manipulation, but can also be solved as is:
the first equation is:
60 = c + 1.5 * c
combine like terms on the right side of the equation to get:
60 = 2.5 * c
divide both sides of the equation by 2.5 to get:
60 / 2.5 = c
solve for c to get:
c = 24 dollars.
the cost of the sweater is 24 dollars.
you now have:
the cost of the sweater is 24 dollars.
the sale price of the sweater is 45 dollars.
the retail price of the sweater is 60 dollars.
that's your solution.
below is a little extra information.
the gross profit is equal to the sale price minus the cost which is equal to 45 minus 24 = 21 dollars.
the gross profit margin is equal to the gross profit divided by the cost which is equal to 21 / 24 = .875 * 100 = 87.5%.
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