Q39. - Algebra 2

Question

For Exercises 39-41, use the following information.

Adam and his family are planning to rent a midsize car for one-day trip. In the Standard Rental Plan, they can rent a car for \(52 per day plus 23 cents per mile. In the Deluxe Rental Plan, they can rent a car for \)80 per day with unlimited mileage. 

39. For each plan, write an equation that represents the cost of renting a car.

Step-by-Step Solution

Answer

The equation that represent cost of renting a car as per Standard Rental plan is $y=23x+52$ and cost of renting a car as per Deluxe Rental plan is $y=80$.

Step-1 – Interpret the data

According to the question, there are two rental plans.

The cost of renting a car as per Standard Rental plan is $52 per day plus 23 cents per mile. In the Deluxe Rental Plan, the cost to rent a car is $80 per day with unlimited mileage. 

Step-2 – Define the variables

Consider two variables x and y.

Denote the cost of renting a car by y and number of miles driven by x.

Step-3 – Build the equations

Let the number of miles driven be x.

In Standard Rental plan car is rented for $52 per day plus 23 cents per mile. Therefore, the cost to rent a car is expressed below. The per day cost is fixed as one-day trip is to be scheduled.

$y=23x+52$

In Deluxe Rental plan car is rented for $80 per day with unlimited mileage. 

Therefore, the cost to rent a car is expressed below. 

$y=80$

Thus, the equation that represent cost of renting a car as per Standard Rental plan is $y=23x+52$ and cost of renting a car as per Deluxe Rental plan is $y=80$.