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The question presents a taxi cab company that charges a flat amount of $5.00 plus a rate of $3.00 per mile traveled. 

We are asked to find the correct equation for determining the number of miles traveled, $ x $, given that the total cost of the fare is $41.00.

### Explanation:

- The total cost of the taxi ride is made up of:
  1. A **flat charge** of $5.00.
  2. An additional **rate of $3.00 per mile traveled**.

If $ x $ is the number of miles traveled, the cost of the miles traveled is $ 3x $, and the total fare equation would be:

\[
\text{Total Cost} = 3x + 5
\]

Given that the total cost is $41.00, the equation becomes:

\[
41 = 3x + 5
\]

This matches the first option.

### Therefore, the correct equation is:
\[
41 = 3x + 5
\]

Would you like further details or have any other questions?

Here are some related questions to expand on this:
1. How would you solve for $ x $ in the equation $ 41 = 3x + 5 $?
2. What is the general form of a linear equation?
3. How does the concept of a flat fee plus a rate apply in other real-world scenarios?
4. How could you graph the equation $ 41 = 3x + 5 $ and interpret it?
5. If the total cost increased to $50.00, what would the new equation look like?

**Tip**: When solving a linear equation, always isolate the variable step by step to maintain accuracy.

A taxi cab company charges a flat amount of $5.00 plus a rate of $3.00 per mile traveled. If the total cost of the fare was $41.00, then which of the following equations can be used to determine the number of miles traveled, x?

This problem involves solving a linear equation to determine the number of miles traveled in a taxi ride. Given a flat fee of $5.00 and a rate of $3.00 per mile, the total fare is $41.00. Learn how to set up and solve this equation. Suitable for students in Grades 7-9.

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