The management of Hartman Rent-A-Car has allocated $1.92 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $16,000 each, intermediate-size cars cost $24,000 each, and full-size cars cost $32,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)

Question

The management of Hartman Rent-A-Car has allocated $1.92 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $16,000 each, intermediate-size cars cost $24,000 each, and full-size cars cost $32,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)

I know x+y+z=100 and 16000x+24000y+32000z=1920000, but what would be the equation for x=?

Answer 1

x = 2 y twice as many compacts as intermediates

Answer 2

Well, since you mentioned that Hartman purchases twice as many compacts as intermediate-size cars, we can set up the equation as follows:

x = 2y

This means that the number of compact cars purchased (x) is twice the number of intermediate-sized cars purchased (y).

Answer 3

To determine the equation for x, we need to consider the given information that Hartman purchases twice as many compacts as intermediate-size cars. Let's denote the number of intermediate-sized cars as "y."

Since Hartman purchases twice as many compacts as intermediate-size cars, the equation for the number of compacts, denoted by "x," would be:

x = 2y

This equation states that the number of compacts (x) is equal to two times the number of intermediate-sized cars (y).

Answer 4

To find the equation for x, let's use the information given in the question:

1) "Hartman purchases twice as many compacts as intermediate-size cars": This implies that the number of compact cars purchased (x) is twice the number of intermediate-sized cars purchased (y). We can express this relationship as x = 2y.

2) "The total number of cars to be purchased is 100": This means that the sum of the number of compact cars (x), intermediate-sized cars (y), and full-size cars (z) is equal to 100. We can represent this as x + y + z = 100.

Now, we can use the equation x = 2y and substitute it into the equation x + y + z = 100 to express x in terms of y:

2y + y + z = 100

Combining like terms:

3y + z = 100

Therefore, the equation representing x in terms of y and z is 3y + z = 100.