Twin Rivers has a population of 90,800, and its population has been increasing by 800 people each year. White Stone has a population of 87,200, and its population has been increasing by 1,200 people each year. These trends in population change are expected to continue. Which equation can you use to find t, the number of years it will take for the two cities to have the same population? Choices: (A)90,800 - 800t = 87,200 + 1,200t (B)90,800 + 800t = 87,200 + 1,200t How long will it take for the two cities to have the same population? Simplify any fractions. ____ years

Question

Twin Rivers has a population of 90,800, and its population has been increasing by 800 people each year. White Stone has a population of 87,200, and its population has been increasing by 1,200 people each year. These trends in population change are expected to continue. Which equation can you use to find t, the number of years it will take for the two cities to have the same population?   Choices: (A)90,800 - 800t = 87,200 + 1,200t (B)90,800 + 800t = 87,200 + 1,200t  How long will it take for the two cities to have the same population? Simplify any fractions.   ____ years

Bytelearn · Accepted Answer

Set Up Equation: Let's set up an equation to represent the populations of Twin Rivers and White Stone after t years. We'll let P_twin and P_white represent the populations of Twin Rivers and White Stone, respectively, after t years. P_twin = 90,800 + 800t P_white = 87,200 + 1,200t We want to find the value of t when P_twin = P_white.Equalize Populations: Now we set the two expressions equal to each other to find when the populations will be the same: 90,800 + 800t = 87,200 + 1,200t This is the correct equation to use, so the answer to the first part of the question is (B)90,800 + 800t = 87,200 + 1,200t.Solve for t: To solve for t, we need to get all the terms with t on one side and the constants on the other side. Let's subtract 800t from both sides: 90,800 + 800t - 800t = 87,200 + 1,200t - 800t This simplifies to: 90,800 = 87,200 + 400tSubtract Constants: Next, we subtract 87,200 from both sides to isolate the term with t: 90,800 - 87,200 = 87,200 + 400t - 87,200 This simplifies to: 3,600 = 400tDivide by 400: Now we divide both sides by 400 to solve for t: 3,600 / 400 = 400t / 400 This simplifies to: t = 9

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