Alright, let's solve this problem step by step. We have two towns with different starting populations and different rates at which they gain or lose population each month.
1) Let's start by focusing on the first town. It has a population of 43,425 people. We are given that 200 people move into town, while 125 people move out each month. This is a net gain of 200 - 125 = 75 people per month.
2) Now let's look at the second town. It has a larger population of 45,000 people. However, this town does not gain anyone each month, and loses 150 people each month. This is a net reduction of 150 people per month.
So, in order to figure out when these two towns will have equal populations, we need to set up an equation:
For the first town: 43,425 (starting population) + 75 (net gain) * months
For the second town: 45,000 (starting population) - 150 (net reduction) * months
3) We set these two equations equal to each other:
43,425 + 75 * months = 45,000 - 150 * months
4) Next, add 150 * months to both sides of the equation to bring all the variables to one side:
43,425 + 75 * months + 150 * months = 45,000
5) simplify that to get:
43,425 + 225 * months = 45,000
6) Next, we'll solve this equation for months. Subtract 43,425 from both sides of the equation to get:
225 * months = 1,575
7) Finally, we'll divide by 225 on both sides to get our answer:
months = 1,575 / 225
The solution is approximately 7 months.
So, after roughly 7 months, both towns will have the same population.