Question

A car rental agency rent compact, midsize, and luxury cars. Its goal is to purchase 48 cars for a total of $932,000 and to earn a daily rental of $ 1,265 from all the cars. The compact cars cost $13,000 each earn $ 20 per day in rental, the midsize cars cost $ 25,000 each earn $ 27 per day, and the luxury cars cost $ 29,000 each and earn $ 45 per day. Your task will be to find the number of each type of car the agency should purchase to meet its goal.

Answer 1

• 25 compact
• 15 midsize
• 8 luxury

Explanation:

The set of relationships can be formulated as three equations in three unknowns. These can be written as an augmented matrix and solved using a calculator.

Let x, y, z represent the numbers of compact, midsize, and luxury cars, respectively. Then the relations are ...

x + y + z = 48 . . . . . . total number of cars purchased

13x +25y +39z = 932 . . . . . total cost in thousands

20x +27y +45z = 1265 . . . . daily rental revenue

The augmented matrix of coefficients looks like ...

`\left[\begin{array}ccc1&1&1&48\\13&25&39&932\\20&27&45&1265\end{array}\right]`

And its solution is ...

(x, y, z) = (25, 15, 8)

The agency should purchase 25 compacts, 15 midsize, and 8 luxury cars.