Mark the number of months as x. Describe the populations of both towns in terms of x to make an equation.
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Practice makes perfect
A town's population is 43 425. We are told that about 125 people move out each month, and on average 200 people move in. A nearby town has a population of 45 000. It has no one moving in and an average of 150 people moving away every months. We want to find in about how many months the populations of these two towns will be equal. Let's start with defining x.
x - the number of months
Let's now express the first and second town's populations in terms of x. The first town has a population of 43 425 minus 125 each month and plus 200 people each month. Therefore, its population will be 43 425 minus the amount of months x multiplied by 125 plus x multiplied by 200. The population of the second town will be 45 000 minus the amount of months x, multiplied by 150.
First population:& 43 425- 125x+ 200x
Second population:& 45 000- 150x
We want these populations to be equal, so we need to make an equation that will have the first population on the left-hand side and the second population on the right-hand side.
43 425- 125x+ 200x = 45 000- 150x
Now, we will solve the obtained equation. We will use inverse operations to combine like terms on both sides of the equals sign and solve for x.
