Question

A​ town's population is 53 comma 350. About 75 people move out of the town each month. Each​ month, 175 people on average move into town. A nearby town has a population of 55 comma 825. 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. Then solve the equation and answer the question.

Answer 1

In about 9 months the population of the towns will be equal.

Explanation:

The population of both cities, after t months, can be modeled by linear functions.

Town A:

Population of 53330.

About 75 people move out of the town each month. Each​ month, 175 people on average move into town.

So, after t months, the population will be:

`A(t) = 53300 + (175 - 75)t`

`A(t) = 53300 + 100t`

Town B:

Population of 55,825.

An average of 175 people moving away every month.

So, after t months, the population will be:

`B(t) = 55825 - 175t`

In about how many months will the populations of the towns be​ equal?

This is t for which:

`A(t) = B(t)`

`53300 + 100t = 55825 - 175t`

`275t = 2525`

`t = (2525)/(275)`

`t = 9.18`

Rounding to the nearest number

In about 9 months the population of the towns will be equal.