Jim needs to rent a car. A rental company charges $21.00 per day to rent a car and $0.10 for every mile driven. • He will travel 250 miles. • He has $115.00 to spend. Write an inequality that can be used to determine d, the maximum number of days that Jim can rent a car. Jim believes the maximum whole number of days he can rent the car is 5. Is he correct? Why or why not? Explain your answer.
Let d be the maximum number of days Jim can rent a car.
The total cost of renting the car for d days and driving 250 miles can be expressed as:
Cost = 21d + 0.10(250)
Jim's total budget is $115.00, so we can set up the inequality:
21d + 0.10(250) ≤ 115
Simplifying and solving for d, we get:
21d + 25 ≤ 115
21d ≤ 90
d ≤ 4.29
Therefore, Jim can rent the car for a maximum of 4 days (since he can't rent a car for a fraction of a day).
Jim's belief that he can rent the car for 5 days is incorrect. This is because if he rents the car for 5 days, the total cost will be:
Cost = 21(5) + 0.10(250) = 105 + 25 = $130.00
This is more than his budget of $115.00, so he can only rent the car for a maximum of 4 days.