Question

A town's population is 62,400, about 75 people move out of the town each month, and about 200 people move into town each month. A nearby town has a population of 65,650, and it has no one moving in and an average of 200 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, then solve the equation.

Answer 1

By setting up an equation 62,400 + 125t = 65,650 - 200t and solving for t, we find that it will take 10 months for the populations of the two towns to be equal.

Step-by-step explanation:

How to Determine When Populations Will Be Equal

We are given that the initial population of the first town is 62,400, with a net increase of 125 people per month (200 people moving in and 75 people moving out). The second town starts with a population of 65,650 and has 200 people moving out each month, with no one moving in.

To find out when the populations will be equal, we can set up an equation where the first town's population (P1) is equal to the second town's population (P2). We use the variable t to represent the number of months in the future.

P1 = 62,400 + 125t

P2 = 65,650 - 200t

Solving the Equation:

Set P1 equal to P2 and solve for t:

62,400 + 125t = 65,650 - 200t

Combining like terms gives us:

325t = 3,250

Dividing both sides by 325 gives:

t = 10

Therefore, it will take 10 months for the populations of the two towns to become equal.