https://file.aiquickdraw.com/mathbot/file/17298131775633iruzpmy.jpg

Let's analyze the situation described in the problem.

We have two towns:
1. **Town A** with a population of **42,975**, where **125 people move out** every month, and **175 people move in** each month.
2. **Town B** with a population of **46,125**, which does not change because no one is moving in or out.

We need to find when their populations will be equal.

Let **m** represent the number of months. After **m** months:
- The population of Town A will be **42,975 - 125m + 175m**.
- The population of Town B will remain **46,125**.

To find when the populations are equal, we need to set the population expressions equal to each other:
\[
42,975 + (175 - 125)m = 46,125
\]

Simplifying:
\[
42,975 + 50m = 46,125
\]

Now, let's solve this equation:
\[
50m = 46,125 - 42,975
\]
\[
50m = 3,150
\]
\[
m = \frac{3,150}{50} = 63
\]

So, the populations will be equal in **63 months**.

Now, looking at the provided options for the equation:
- The correct equation should be **175m - 125m + 42,975 = 46,125**, which simplifies to **50m + 42,975 = 46,125**.

This matches **option C** in the image.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. How would the equation change if 200 people moved into Town A each month?
2. What if Town B's population also increased by 50 people each month?
3. How many months would it take if the population of Town A started at 50,000 instead of 42,975?
4. What is the population difference between the towns after 30 months?
5. How would the result change if 175 people moved out of Town A instead?

**Tip:** When solving for unknowns, carefully align the change rate per month for each town and simplify before equating.

A town's population is 42,975. About 125 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 46,125. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation.

Solve a linear equation model for population growth and decline involving two towns with a population difference. This problem illustrates how to balance inflows and outflows in population changes using algebraic equations. Suitable for Grades 8-10.

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