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Let's work through the problem.

The task is to write two equations representing the total daily rental costs of Company A and Company B, based on the number of miles driven.

The costs are given as follows:
- **Company A**: $39.95 per day + $0.79 per mile
- **Company B**: $59.95 per day + $0.29 per mile

Let **m** represent the number of miles driven, **A** represent the total cost of renting from Company A, and **B** represent the total cost of renting from Company B.

### Equations:
1. **Company A**:  
   \[
   A = 39.95 + 0.79m
   \]
2. **Company B**:  
   \[
   B = 59.95 + 0.29m
   \]

Next, the problem asks to evaluate these equations at specific values of **m**:
- For **Company A**, evaluate when **m = 37**.
- For **Company B**, evaluate when **m = 42**.

### Evaluating the equations:
- **For Company A** when **m = 37**:  
   \[
   A = 39.95 + 0.79(37)
   \]

- **For Company B** when **m = 42**:  
   \[
   B = 59.95 + 0.29(42)
   \]

I will now calculate these values.The evaluated costs are as follows:

- **For Company A** when $ m = 37 $: The total cost is **$69.18**.
- **For Company B** when $ m = 42 $: The total cost is **$72.13**.

Let me know if you need more details or have any questions.

Here are 5 related questions to expand on this topic:
1. What is the break-even point where both companies would cost the same?
2. How would the cost for Company A change if you drive 50 miles instead?
3. What would be the total cost for Company B if you drive 100 miles?
4. How does the daily rate affect the total cost if no miles are driven?
5. Can you graph the two equations to compare costs visually?

**Tip:** When comparing rental options, always consider the fixed daily rate and the per-mile rate to determine the better option based on your expected mileage.

You just rented a new apartment and need to move your belongings. You contact two rental companies and receive information for the one-day cost of renting a moving van. Write two equations to represent the cost for each company based on miles driven, and evaluate the cost for specific mileages.

Learn how to calculate the daily cost of renting a moving van based on mileage. This example compares two companies with different daily and per-mile rates. Suitable for students in Grades 8-10.

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