A national rental car company purchased compact and midsize cars. The company budgeted $14,000,000 to buy a minimum of 650 cars altogether. The company did not exceed their budget. The company paid an average of $13,000 for each compact car and $28,000 for each midsize car. Which system of inequalities represents all possibilities for the number of compact cars, c, and the number of midsize cars, m, that could have been bought?

In the question, we are given that a national rental car company purchased compact and midsize cars. The company budgeted $14,000,000 to buy a minimum of 650 cars altogether. The company did not exceed its budget. The company paid an average of $13,000 for each compact car and $28,000 for each midsize car.

We are asked to give the system of inequalities that represents all possibilities for the number of compact cars, c, and the number of midsize cars, m, that could have been bought.

Given that c is the number of compact cars, and m is the number of midsize cars, the total number of cars can be shown as c + m.

But, we are also told that the minimum number of cars bought is 650.

Thus, we get an inequality c + m ≥ 650.

The cost of buying one one compact car = $13,000.

The number of compact cars bought = c.

Thus, the cost of c number of compact cars = $13,000c.

The cost of buying one one midsize car = $28,000.

The number of midsize cars bought = m.

Thus, the cost of m number of midsize cars = $28,000m.

Thus, the total cost is shown as: $13000c + $28000m.

But, the total cost needs to be less than the budget of the company, $14,000,000 .

Thus, we get an inequality,

13000c + 28000m ≤ 14000000

Dividing by 100, we get:

13c + 28m ≤ 140000.

Thus, the system of inequalities representing the given situation is:

c + m ≥ 650, and 16c 28m = 14000.

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