The problem asks you to write an equation for the total cost $C$, in terms of the number of miles driven $m$, for renting a truck. Here's how to set up the equation based on the provided information:

• There is an initial charge of $40 for the truck rental.
• There is an additional fee per mile driven.
• When Sophie drives 5 miles, the total cost is $55.

Step-by-step solution:

1. Initial charge: $40 (fixed cost).
2. Let the cost per mile be $x$.
3. When Sophie drives 5 miles, the total cost is $55. So we can set up the following equation: $40 + 5x = 55$
4. Solve for $x$: $5x = 55 - 40$ $5x = 15$ $x = 3$ Therefore, the cost per mile is $3.

Final equation:

Now that we know the cost per mile is $3, the total cost equation in terms of $m$ miles driven is: $C = 40 + 3m$

Would you like further details or have any questions?

Related Questions:

1. What would the total cost be if Sophie drives 10 miles?
2. How does the total cost change as $m$ increases?
3. What if the initial charge was $50 instead of $40? How would that affect the equation?
4. Can you generalize this equation for any initial charge and cost per mile?
5. How would you calculate the total cost if Sophie were to drive $m$ miles but the cost per mile changed to $2.50?

Tip:

When dealing with word problems, always identify the fixed and variable components first to help set up your equation correctly.