https://file.aiquickdraw.com/mathbot/file/1726379326871gwawnn18.jpg

Let's address part (c) of the problem step by step.

The problem asks to find the maximum number of whole hours where renting from **Cannon Cars** is a cheaper option than **Jet Cars**.

### Given:
- **Cannon Cars** charges a non-refundable deposit of **$30** and **$5.50** per hour.
- **Jet Cars** charges **$10** per hour with no deposit.

### Expressions for total charges:
1. **Cannon Cars** total cost $ C $:
   \[
   C = 30 + 5.50t
   \]
   where $ t $ is the number of hours.
   
2. **Jet Cars** total cost $ J $:
   \[
   J = 10t
   \]

### Part (c) requirement:
We need to find the maximum number of whole hours $ t $ such that the cost of Cannon Cars $ C $ is cheaper than the cost of Jet Cars $ J $. This leads to the inequality:
\[
30 + 5.50t < 10t
\]

### Solve the inequality:
\[
30 + 5.50t < 10t
\]
Subtract $ 5.50t $ from both sides:
\[
30 < 4.50t
\]
Divide both sides by 4.50:
\[
t > \frac{30}{4.50}
\]
\[
t > 6.67
\]

Since we are asked for the maximum number of **whole hours**, $ t $ must be an integer. The largest whole number less than 6.67 is **6**.

### Conclusion:
The maximum number of whole hours for which **Cannon Cars** is a cheaper option than **Jet Cars** is **6 hours**.

Would you like more details on the solution or have any questions?

---

Here are 5 related questions for further exploration:
1. What would be the total cost for Cannon Cars if the rental was for 8 hours?
2. How would the deposit of Cannon Cars affect shorter rentals compared to Jet Cars?
3. For how many hours of rental would both companies charge the same amount?
4. If Jet Cars reduced its hourly rate to $9, how would the comparison change?
5. What would be the total cost for Jet Cars after 10 hours?

**Tip**: Always consider fixed costs (like deposits) when comparing options for short-term and long-term scenarios.

Find the maximum number of whole hours of renting a car from Cannon Cars for its services to be a cheaper option.

Learn how to solve an inequality to find the maximum number of hours for which Cannon Cars is a cheaper option compared to Jet Cars. This problem involves solving inequalities and comparing pricing structures, suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation