Roland2rule wrote:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

A) $5,000 and $1,000
B) $9,000 and $5,000
C) $11,000 and $9,000
D) $15,000 and $5,000
E) $20,000 and $10,000

OA is D
I'm struggling with the question, can an expert explain why it is D? Thanks a lot.

Say the price of the first car = $x, and that of the second car = $y.

Thus, the sale price of the first car = (100 + 10)% of x = 1.1x and the sale price of the second car = (100 - 10)% of y = 0.9y

Profit margin from the sale of the two cars = Sale price of the two cars - Cost price of the two cars = (1.1x + 0.9y) - (x + y) = 0.1 (x - y) ---(1)

We know that the profit margin is 5% (of the cost price) = 0.05(x + y) ---(2)

We are given that the dealership's total profit was $1000, thus

0.1 (x - y) = 1000 => x - y = 10,000 ---(3)

Also, 0.05(x + y) = 1000 => x + y = 1000/0.5 = 20,000 ---(4)

From (3) and (4), we get that x= $15000 and y = $5000.

The correct answer: D

Hope this helps!

-Jay
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