Question

A used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a loss of 20 percent of the dealer's purchase price for that car.

If the dealer sold each car for $20,000, what was the dealer's total profit or loss, in dollars, for the two transactions combined?

A. 1000 profit
B. 2000 profit
C. 1000 loss
D. 2000 loss
E. 3334 loss

Answer 1

C. 1000 loss.

Explanation:

Let x represent purchase price of each car.

We have been given that a used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a loss of 20 percent of the dealer's purchase price for that car.

We can represent the car that dealer sold with 25% profit to find purchase price as:

`x+0.25x=20,000`

`1.25x=20,000`

`(1.25x)/(1.25)=(20,000)/(1.25)`

`x=16,000`

Therefore, the purchase price of 1st car was $16,000.

We can represent the car that dealer sold with 20% loss to find purchase price as:

`x-0.20x=20,000`

`0.80x=20,000`

`(0.80x)/(0.80)=(20,000)/(0.80)`

`x=25,000`

Therefore, the purchase price of 2nd car was $25,000.

The total purchase price of both cars would be
`16,000+25,000=41,000`

The total sale price of both cars
`20,000+20,000=40,000`.

We can see that the sale price of both car is less than purchase price by $1000, so the dealer got a loss of $1000.

Therefore, the dealer's total loss, in dollars, for the two transactions combined was 1000 and option C is the correct choice.