Please explain why this this does not break even

Question

If a used car salesman sells TWO cars at $6000 each, making a profit of 20% on one and taking a loss of 20% on the other, then at end of day, would she break even? make $$? or lose $$? (and by how much)? 

Answer 1

Hi Kelvin,

 

I like your temperature scale. :-)

 

A car that is sold for $6000 and yields a 20% profit, means that the dealer bought the car for a lower price than $6000 and 20% of that lower price is added to it to get $6000.

 

A car that is sold for $6000 at a 20% loss, means that the dealer bought the car for more than $6000 and lost 20% of that higher price.

 

20% of a bigger number is more than 20% of a smaller number so the dealer lost money.

 

To figure the profit, let X = the original purchase price.

 

Then X + 0.2X = 6000

 

1.2X = 6000

 

X = $5000 and the dealer made a profit of $1000

 

To figure the loss, let X = the original purchase price

 

Then X - 0.2X = 6000

 

0.8X = 6000

 

X = $7500 and the dealer lost $1500

 

Subtracting his $1000 profit means that he had a net loss of $500.

 

Dan

Answer 2

$6000 car at a profit of 20%

120%*c=6000

1.2*c=6000

12*c=60,000

c=60,000/12

c=$5000 was the cost of the car and she sells it for $6000 and makes $1000

$6000 car at a loss of 20%

she sold the car for only 80% of the cost so she lost 20%

80%*c=6000

0.8c=6000

8c=60,000

c=60,000/8

c=$7500 was her cost and she sold the car for $6000 so she lost $1500

if she loses $1500 and makes $1000 then she did not break even; she lost $500  (-$1500+$1000=-$500)