Question

A town's population is 39,000. About 75 people move out of the town each month. Each month, 125 people on average move into town. A nearby town has a population of 40,200. It has no one moving in and an average of 150 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

Let x be the amount of months.

For the first town, the equation would be 125x-75x+39,000.

For the second town, the equation would be 40,200-150x.

To find x, we first make them equal to each other.

125x-75x+39,000 = 40,200-150x

Now we can solve for x.

125x-75x+39,000 = 40,200-150x

Add the like terms and isolate x.

200x = -1200

Now just divide both side by 200 and you get x = -6

Hence in 6 months, the towns population would be equal.

Answer 2

Answer:

6 Months

Step-by-step explanation:

Let's first tally up the net gains and losses of the towns.

The first one, we'll just call it Town A, loses 75 and gains 125. 125-75=50,     this means that Town A gains 50 people each month

Town B however, gains nothing and loses 150. Town B loses 150 per month.

Overall, they reduce the gap between them by 200 people every month.

The difference between them (40200-39000) is 1200 people.

We can divide that by 200 for our final answer, which is 6.

In 6 months, the towns' populations will be equal.