Question

A town's population is 43,875. About 100 people move out of the town each month. Each month, 125 people on average move into town. A nearby town has a population of 45,000. 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 and answer the question, Which equation models the situation?

A. 125m + 100m + 45,000 = 43,875 + 200m
B. 125m + 100m + 43,875 = 45,000 + 200m
C. 125m - 100m + 45,000 = 43,875 - 200m
D. 125m - 100m + 43,875 = 45,000 - 200m

Answer 1

To find the number of months it will take for the populations of the towns to be equal, set up an equation. The equation 43875 - 100m = 45000 - 200m models the situation. Solving the equation, it will take approximately 45 months for the populations to be equal.

Step-by-step explanation:

To find the number of months it will take for the populations of the towns to be equal, we can set up an equation. Let m be the number of months.

In the first town, the population decreases by 100 each month and increases by 125 each month in the second town.

Therefore, the equation is: 43875 - 100m = 45000 - 200m.

To solve this equation, we can start by simplifying it: 125m - 100m = 45000 - 43875.

Combining like terms, we get: 25m = 1125. Dividing both sides by 25, we find that m = 45.

Therefore, it will take approximately 45 months for the populations of the towns to be equal.

The correct equation that models the situation is (B) 125m + 100m + 43875 = 45000 + 200m.