Bunuel wrote:

A car dealership orders 80 automobiles from the factory and wants to sell each for $22,275. 60 of the cars are sold at this price, which represented an 8% profit above the dealership’s cost from the factory. To sell the remaining 20 cars, the dealership has to substantially discount the retail price, and each is sold at a price that represents a 4% loss below the dealership’s cost. What was the dealership’s profit or loss as a percent of the dealership’s initial cost for the 80 automobiles?

A. 5% loss

B. 4% loss

C. 2% profit

D. 4% profit

E. 5% profit

We are given that 60 cars were sold for $22,275 at a profit of 8%. Thus:

Profit = 0.08(cost)

Revenue - cost = 0.08(cost)

22,275 - c = 0.08c

22,275 = 1.08c

22,275/1.08 = c

20,625 = c

Thus, the dealership’s cost for each car was 20,625 dollars.

We are also given that 20 cars were sold at a loss of 4%. Thus, each of the remaining 20 cars was sold at 96% of the dealership’s cost.

Thus, each of the remaining 20 cars was sold for 0.96(20,625) = $19,800.

In total, the dealership spent 20,625 x 80 = 1,650,000 on the cars and earned:

22,275 x 60 + 19,800 x 20 = 1,336,500 + 396,000 = 1,732,500

Thus, the dealership made a profit on the sale of 80 cars and the profit is:

[(1,732,000 - 1,650,000)/1,650,000] x 100 = (82,000/1,650,000) x 100 = 0.05 x 100 = 5%.

Answer: E

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