GMAT Practice Question: 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?
- 10 dollars
- 16 dollars
- 20 dollars
- 24 dollars
- 25 dollars
Topics: word problems, percentages, profit/loss, translations
Solution
Step 1
We create unknowns for the retailer's cost and the retailer's gross profit
C = \text{cost of the appliance} P = \text{gross profit on the appliance}
Step 2
We translate \textbf{\text{"gross profit on the appliance was 25 percent of the retailer's cost"}} into a percentage relationship
P = \frac{25}{100} \times C
Step 3
We set the selling price equal to the sum of cost and profit
80 = C + \frac{25}{100} \times C
Step 4
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
Step 5
We calculate the gross profit by finding 25% of the cost
P = \frac{25}{100} \times 64 = \frac{1}{4} \times 64 = 16
Answer
16
