A retailer sold an appliance for 80 dollars. If the retailer's gross profit on the appliance was...

Question

A retailer sold an appliance for 80 dollars. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?

GMAT Panda · Accepted Answer

16 We create unknowns for the retailer's cost and the retailer's gross profit C = cost of the appliance P = gross profit on the appliance We translate "gross profit on the appliance was 25 percent of the retailer's cost" into a percentage relationship P = 25/100 C We set the selling price equal to the sum of cost and profit 80 = C + 25/100 C We combine like terms and solve for C by isolating the variable C + 25/100C = 80 125/100C = 80 C = 80 100/125 = 64 We calculate the gross profit by finding 25% of the cost P = 25/100 64 = 1/4 64 = 16

Explanation	Calculations	Help
$We create unknowns for the retailer's cost and the retailer's gross profit$	$C = cost of the appliance P = gross profit on the appliance$
$We translate "gross profit on the appliance was 25 percent of the retailer’s cost" into a percentage relationship$	$P = \frac{25}{100} \times C$
$We set the selling price equal to the sum of cost and profit$	$80 = C + \frac{25}{100} \times C$
$We combine like terms and solve for C by isolating the variable$	$C + \frac{25}{100} C = 80 \frac{125}{100} C = 80 C = 80 \times \frac{100}{125} = 64$
$We calculate the gross profit by finding 25% of the cost$	$P = \frac{25}{100} \times 64 = \frac{1}{4} \times 64 = 16$

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