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The question in the image asks to solve for the constant rate per minute and the fixed monthly fee charged by a cell phone carrier based on the provided data.

### Given:
- In January, for 175 minutes, the total cost is $60.5.
- In February, for 300 minutes, the total cost is $68.

Let:
- $ x $ be the fixed monthly fee.
- $ r $ be the constant rate per minute.

We can create two equations from the given information:

1. $ x + 175r = 60.5 $
2. $ x + 300r = 68 $

Now, let's solve this system of equations to find $ x $ and $ r $.

### Step 1: Subtract equation 1 from equation 2:
\[
(x + 300r) - (x + 175r) = 68 - 60.5
\]
\[
300r - 175r = 7.5
\]
\[
125r = 7.5
\]
\[
r = \frac{7.5}{125} = 0.06
\]

Thus, the constant rate per minute is **$0.06**.

### Step 2: Substitute $ r = 0.06 $ into one of the original equations:
Using the first equation:
\[
x + 175(0.06) = 60.5
\]
\[
x + 10.5 = 60.5
\]
\[
x = 60.5 - 10.5 = 50
\]

Thus, the fixed monthly fee is **$50**.

### Final Answer:
- The constant charge per minute is **$0.06**.
- The fixed monthly fee is **$50**.

Would you like further explanation or details on any step?

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Here are five related questions to extend your understanding:
1. How do you solve systems of linear equations with substitution and elimination methods?
2. What are the different ways to express a linear relationship between two variables?
3. How would the solution change if the total costs were different?
4. Can you graph the two equations to visually represent the solution?
5. How can linear equations be used in other real-world applications like budgeting or planning?

**Tip:** When solving systems of equations, always check your solutions by substituting them back into the original equations to ensure they satisfy both.

A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. In January, the total cost for 175 minutes was $60.5, while in February, the total cost for 300 minutes was $68. The constant charge for each minute used is: $0.07, $0.08, or $0.06. Part 2: The fixed monthly fee charged by the carrier is: ___.

Learn how to solve a system of linear equations to determine the fixed monthly fee and the constant rate per minute for a cell phone carrier. This problem involves two linear equations based on total costs for different usage durations. Suitable for Grades 9-11.

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