We are given that the taxi company charges a pick-up fee of $3.60 and an additional $5 per mile. The total fare is $18.60 (not including the tip), and we are asked to find an equation that represents the number of miles traveled, denoted by $x$.

The correct equation can be formed as follows:

• The total fare is the sum of the pick-up fee and the cost per mile for $x$ miles.
• The total cost is therefore:
  $3.60 + 5x = 18.60$ This equation says that the fare is the pick-up fee of $3.60 plus $5 for each mile traveled, for a total of $18.60.

Now, let's check the answer options:

• A: $18.6 = 5(3.6 + x)$ — Incorrect. This equation adds the pick-up fee inside the parentheses as if it’s multiplied by 5, which is not true.
• B: $5 + 3.6x = 18.6$ — Incorrect. This equation switches the pick-up fee and mileage costs, and the units for $5 and $3.60 are applied incorrectly.
• C and D: These don't correspond to valid algebraic equations.

Thus, none of the given options correctly represent the context. The correct equation should be: $3.6 + 5x = 18.6$

Do you need more details or have any questions?
Here are 5 follow-up questions you might find useful:

1. How can we solve the equation $3.6 + 5x = 18.6$ to find $x$?
2. What does the slope (5) in this context represent?
3. How do tape diagrams differ from algebraic equations in representing word problems?
4. What steps are needed to check if an equation matches a real-world problem?
5. Could you create an equation if the fare structure changed, say $4 per mile and a $6 pick-up fee?

Tip: When translating word problems to algebraic equations, carefully match operations (like addition or multiplication) to the problem's descriptions.