Question

At the start of the millennium, State A was the third most populous state in the country, followed by State B. Since that time, State B has expenienced faster growth. The population y (in millions) of the given state in year x is approximated by the following equations, where x=0 corresponds to the year 2000 . In what yoar did State B overtake State A in population? To the nearest million, what was the population of these states at that time? State B: 8y−3x=137 State A: 14y−x=295 The year State B overtook State A was (Type a whole number) The population at that time was million.

Answer 1

To find the year when State B overtook State A in population, we need to solve the given equations simultaneously and find the values of x and y that satisfy both equations.

State B: 8y - 3x = 137

State A: 14y - x = 295

We can use the method of substitution to solve this system of equations. Rearranging the equations, we have:

State B: 3x = 8y - 137 (equation 1)

State A: x = 14y - 295 (equation 2)

Substitute equation 2 into equation 1:

3(14y - 295) = 8y - 137

Simplify and solve for y:

42y - 885 = 8y - 137

42y - 8y = 885 - 137

34y = 748

y = 748/34

y ≈ 22

Now, substitute the value of y back into equation 2 to find the corresponding x value:

x = 14(22) - 295

x = 308 - 295

x = 13

Therefore, State B overtook State A in population approximately 13 years after the year 2000, which corresponds to the year 2013.

To find the population at that time, we substitute the values of x and y into either equation. Let's use equation 2:

x = 14y - 295

x = 14(22) - 295

x = 308 - 295

x = 13

The population at that time (year 2013) was approximately 13 million.

Therefore, the year when State B overtook State A in population was 2013, and the population at that time was approximately 13 million.

Step-by-step explanation:

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