Question

City A's population is 68,000, decreasing at a rate of 80 people per year. City B, having a population of 42,000, is increasing at a rate of 120 people per year. In how many years will both cities have the same population?

(a) 100 years
(b) 200 years
(c) 300 years
(d) 400 years

Answer 1

It will take 130 years for both cities to have the same population.

Step-by-step explanation:

To find out how many years it will take for both cities to have the same population, we need to set up an equation.

Let x be the number of years it will take for both cities to have the same population.

For City A, the population is decreasing at a rate of 80 people per year. So, the population after x years will be 68,000 - 80x.

For City B, the population is increasing at a rate of 120 people per year. So, the population after x years will be 42,000 + 120x.

Setting the populations of both cities equal to each other, we get:

68,000 - 80x = 42,000 + 120x

Collecting like terms and solving for x, we get:

200x = 26,000

x = 130

Therefore, it will take 130 years for both cities to have the same population.