Management Decisions

Question

The management of Hartman Rent A Car has allocated 1 million dollars in order to buy a fleet of new automobiles. They will be purchasing compact ($8000/per car), intermediate ($12,000/per car), and full size ($16,000/per car). If management purchases twice as many compact cars as they do intermediate, and they purchase 100 total cars, how many of each car was purchased? (You must use the entire budget)

Answer 1

 

 

Answer 2

Let x = the number of intermediate cars purchased.  The number of compact cars is 2x (twice as many).  Since 100 cars were bought in total, the amount of full sized cars that were bought is 100-(x+2x) = 100-3x.

 

$1,000,000 = ($8000)(2x) + ($12,000)(x) + ($16,000)(100-3x)

 

$1,000,000 = 16,000x + 12,000x + 1,600,000 - 48,000x

 

$1,000,000 = -20,000x + 1,600,000

 

-$600,000 = -20,000x

 

Solve for x, the number of intermediate cars.  Once you have x, the number of compacts is 2x and the number of full-sized cars is 100-3x.