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A rental car company charges $40 per day to rent a car and $0.08 for every mile driven. Justin wants to rent a car, knowing that:

He plans to drive 125 miles.
He has at most $170 to spend.

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

3 answers

To find out how many days Justin can afford to rent the car while staying within his budget, we can create an inequality based on the rental car company's charges.

The cost to rent the car consists of two parts:

  1. A daily rental fee of $40 per day.
  2. A mileage fee of $0.08 for every mile driven.

Given that Justin plans to drive 125 miles, we can calculate the total mileage cost:

\[ \text{Mileage Cost} = 0.08 \times 125 = 10 \]

This means that Justin will pay $10 for mileage.

Next, let \( x \) be the number of days Justin rents the car. The total cost \( C \) of renting the car can be expressed as follows:

\[ C = 40x + 10 \]

Justin has at most $170 to spend, so we can set up the inequality:

\[ 40x + 10 \leq 170 \]

Now, we can solve the inequality for \( x \):

  1. Subtract 10 from both sides:

\[ 40x \leq 160 \]

  1. Divide both sides by 40:

\[ x \leq 4 \]

Thus, the solution to the inequality indicates that Justin can rent the car for at most \( \boxed{4} \) days while staying within his budget.

Inequality:
x:

The inequality we derived is:

\[ 40x + 10 \leq 170 \]

If we simplify it to express it in terms of \( x \), we have:

\[ x \leq 4 \]

This means that the number of days \( x \) that Justin can rent the car must be at most 4.

So, the inequality with respect to \( x \) is:

\[ x \leq 4 \]

If you have any further questions or need more assistance, feel free to ask!