Question

If a towns population is 43,650 and 75 people move out each month but 125 people move in each month, and a town near has a population of 45,225 and 125 people move out each month no one moves in how many months until they have the same population?

Answer 1

It will take 160 months for both towns to have the same population.

Step-by-step explanation:

• The first town's population decreases by 75 each month due to people moving out and increases by 125 due to incoming residents, resulting in a net increase of 50 people per month (125 in - 75 out = 50 net increase). The second town's population decreases by 125 each month with no incoming residents, resulting in a net decrease of 125 people per month.

• To find when both towns will have the same population, we need to calculate the difference in their populations and then divide that by the net change in population per month (which is 50, the difference between 125 and 75).

• The initial difference in population between the towns is 45,225 - 43,650 = 1,575 people. Dividing this by the net change in population per month (50 people) gives us 1,575 / 50 = 31.5 months. However, this only accounts for the net change in population, not the exact matching of populations.

• In those 31.5 months, the first town gains 50 people more each month than the second town loses. To account for the exact matching of populations, we need to multiply the 31.5 months by the net gain/loss difference, which is 50 people. Therefore, 31.5 months * 50 people/month = 1,575 people, equal to the initial population difference. Thus, it will take an additional 31.5 months to match precisely. Adding these together gives us a total of 31.5 months + 31.5 months = 63 months for both towns to reach the same population.