Solve for d in inequalities in context

Question

A rental car company charges $22 per day to rent a car and $0.08 for every mile driven. Samuel wants to rent a car, knowing that:

1. He plans to drive 450 miles.
2. He has at most $80 to spend.

Write and solve an inequality which can be used to determine xx, the number of days Samuel can afford to rent while staying within his budget.

Answer 1

Let's set up the inequality step-by-step.

1. Identify the cost components:
2. Daily rental rate: $22 per day
3. Mileage rate: $0.08 per mile
4. Set up the cost expression:
5. The cost for renting the car for d days is 22d
6. The cost for driving 450 miles is 0.08×4500 dollars.

Let's calculate the cost for driving 450 miles: 0.08×450=36

1. Formulate the total cost inequality:
2. Total cost C for d days is: C=22d+36

Samuel wants to spend at most $80, so: 22d+36≤80

1. Solve the inequality:

22d+36≤80

d≤44/22=2

So, Samuel can afford to rent the car for at most 2 days while staying within his $80 budget.