Question

The population growth (in thousands) for Decatur can be represented by the expression 3x + 5 3 x + 261, where x represents the number of years since 2016. The population growth (in thousands) for neighboring Lithonia can be represented by the expression 4x - 5 2 x + 212, where x represents the numberof years since 2016. The governor of Georgia would like to know when the populations of the two towns will be equal.

Answer 1

The problem posed is algebraic and requires setting the population growth expressions of two towns equal and solving for the number of years until they have the same population, which is found to be 49 years after 2016.

Step-by-step explanation:

The student is asking for help in solving a mathematical problem related to population growth in two towns, which involves setting two algebraic expressions equal to each other and finding the value of x that makes them equal. This type of problem requires knowledge of algebra and is often encountered in high school mathematics.

To solve the problem, one would set the expression that represents the population growth of Decatur, which is 3x + 261, and the expression that represents the population growth of Lithonia, which is 4x + 212, equal to one another and solve for x. By finding the value of x at which these two expressions are equal, we can determine the number of years since 2016 when the population of Decatur equals that of Lithonia.

The solution involves creating an equation 3x + 261 = 4x + 212 and solving for x. Subtract 3x from both sides to get 261 = x + 212, then subtract 212 from both sides to isolate x, which gives us x = 49. Therefore, the populations of the two towns will be equal 49 years after 2016, which is in the year 2065.

Answer 2

1967 or 2069

Step-by-step explanation:

To do this, you need to equal the expressions:

3x^2+53x+261=4x^2-52x+212

now, solve for y, when x=0:

-1(0)^2+53(0)+261=4(0)^2-52(0)+212

0+0+261=0-0+212

261=212

the difference is 49, so 49 years before or after 2016.

i think i did this right, if not im sorry bc im tired