In order to get an equation that lets us determine the number of years, we need to find an equation for each population and then make them equal.
• For Canton
For the population of Canton we can formulate the following expression:
Population = initial population + Population increase
We are told that the initial population was 7,720, that is at the year 0, the population was equal to 7,720, then we can rewrite our equation for the population in Canton like this:
Population = 7,720 + population increase
Then we are told that each year the population increases at a rate of 80 people per year, then the population increases it this rate (80) multiplied by the number of years, we call "x" to the number of years, then we can rewrite the equation like this:
Population = 7,720 + 80x
• For Holly Spring
Similarly, for the population in Holly Spring we can formulate the following equation:
Population = initial population + Population increase
In this case, the initial population equals 3,200 and the population increases at a rate of 120 people a year, then we can rewrite our equation to get:
Population = 3,200 + 120x
Now that we have the equations that represent the population in each city, we just have to make them equal, then we get:
Population in Canton = Population in Holly Spring
7,720 + 80x = 3,200 + 120x
We can simplify this equation like this:
7,720 - 7,720