Tim and Jessica plan to rent a camper van for a vacation. To rent the van there is an initial fee of $183
. Additionally, they will be charged $0.39
 per mile where the first 120
 miles are free. The total price Tim and Jessica paid to rent the camper van was $598.74
.

 

Which equation models the cost of the rental van in terms of miles,  m
, traveled for Tim and Jessica's trip?

	
598.74=183+0.39(m−120)

	
598.74=183+m(0.39+120)

	
598.74=0.39m+(183−120)

	
598.74=183+0.39m

The equation that models the total cost of the camper van rental in terms of miles, $ m $, traveled for Tim and Jessica's trip is:

\[
598.74 = 183 + 0.39(m - 120)
\]

### Explanation:
- **183**: This is the initial fee.
- **$ m $**: This represents the total miles traveled.
- **120 miles free**: The first 120 miles don't incur any charge, so the charge only applies to $ m - 120 $ miles.
- **$ 0.39 $**: This is the cost per mile after the first 120 miles.
- **$ 598.74 $**: This is the total amount they paid.

This is why the correct equation is:

\[
598.74 = 183 + 0.39(m - 120)
\]

Do you want more details on how to manipulate this equation, or have any questions? 

Here are 5 related questions:
1. What would the total cost be if they traveled 200 miles?
2. How many miles did they travel if the total cost was $598.74?
3. What would the total cost be if the cost per mile increased to $0.50?
4. How much would they pay if they traveled only 100 miles?
5. What would be the total cost if the initial fee increased to $250?

**Tip:** When solving word problems, it's useful to define variables and break down each component of the cost step by step.

Tim and Jessica plan to rent a camper van for a vacation. To rent the van there is an initial fee of $183. Additionally, they will be charged $0.39 per mile where the first 120 miles are free. The total price Tim and Jessica paid to rent the camper van was $598.74. Which equation models the cost of the rental van in terms of miles, m, traveled for Tim and Jessica's trip?

Learn how to model the total cost of renting a camper van with an initial fee of $183 and a charge of $0.39 per mile after the first 120 miles. This algebra problem provides a step-by-step breakdown of how to form and solve a linear equation based on real-world costs. Suitable for students in Grades 8-10.

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