Questions: Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of 50, and then they charge her 9 per hour. She has 200 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.) 17 hours 22 hours 16 2/3 hours 16 hours

Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of 50, and then they charge her 9 per hour. She has 200 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.)
17 hours
22 hours
16 2/3 hours
16 hours

Transcript text: Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $\$ 50$, and then they charge her $\$ 9$ per hour. She has $\$ 200$ available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.) 17 hours 22 hours $16 \frac{2}{3}$ hours 16 hours

Solution

Solution Steps

To determine the greatest number of hours Esmerelda can rent the car, we need to set up an inequality. The total cost is the sum of the initial fee and the hourly charge multiplied by the number of hours. We need to ensure this total cost does not exceed her budget of $200. Solve the inequality for the number of hours and ensure the result is a whole number since the car cannot be rented for part of an hour.

Step 1: Set Up the Inequality

Esmerelda's total cost for renting the car can be expressed as: \[ \text{Total Cost} = 50 + 9h \] where $ h $ is the number of hours she rents the car. We need to ensure that this total cost does not exceed her budget of $200: \[ 50 + 9h \leq 200 \]

Step 2: Solve the Inequality

To find the maximum number of hours $ h $, we first isolate $ h $ in the inequality: \[ 9h \leq 200 - 50 \] \[ 9h \leq 150 \] Now, divide both sides by 9: \[ h \leq \frac{150}{9} \] Calculating $ \frac{150}{9} $ gives: \[ h \leq 16.6667 \]

Step 3: Determine the Greatest Whole Number of Hours

Since the car cannot be rented for part of an hour, we take the greatest whole number less than or equal to $ 16.6667 $, which is 16.