a rental car company charges $30.42 per day to rent a car and $0.06 for every mile driven. ariana wants to…

a rental car company charges $30.42 per day to rent a car and $0.06 for every mile driven. ariana wants to rent a car, knowing that:\n• she plans to drive 450 miles.\n• she has at most $200 to spend.\nwhat is the maximum number of days that ariana can rent the car while staying within her budget?

a rental car company charges $30.42 per day to rent a car and $0.06 for every mile driven. ariana wants to rent a car, knowing that:\n• she plans to drive 450 miles.\n• she has at most $200 to spend.\nwhat is the maximum number of days that ariana can rent the car while staying within her budget?

Answer

Explanation:

Step1: Calculate the cost for miles driven

The cost for driving 450 miles at $0.06 per mile is (450\times0.06). $$450\times0.06 = 27$$

Step2: Set up the inequality for the total cost

Let (d) be the number of days. The total cost (C) is the sum of the cost for days and the cost for miles. So (C=30.42d + 27). Since she has at most $200 to spend, we have the inequality (30.42d+27\leq200).

Step3: Solve the inequality for (d)

First, subtract 27 from both sides: (30.42d+27 - 27\leq200 - 27) (30.42d\leq173) Then divide both sides by 30.42: (d\leq\frac{173}{30.42}\approx5.69)

Since (d) represents the number of days and it must be an integer, we take the floor of 5.69.

Answer:

5