Question

According to projections through the year​ 2030, the population y of the given state in year x is approximated by State​ A: minus3xplusyequals11 comma 400 State​ B: minus138xplusyequals8 comma 000 where xequals0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same​ population?

Answer 1

In year 2026 population of both the states will be same.

Explanation:

It has been given in the question that the population y of State A in year x will be represented by the equation

-3x + y = 11,400

⇒ y = 11,400 + 3x --------(1)

Similarly, equation that represents the population for State B is

-138x + y = 8,000

⇒ y = 138x + 8,000 -------(2)

If population y for both the states are equal then

3x + 11,400 = 138x + 8,000

11400 - 8000 = 138x - 3x

135x = 3400

`x=(3400)/(135)`

x = 25.19 [After 25 years ]

Since x = 0 represents the population of the states in year 2000

therefore, population y will be same in both the states in year (2000 + 26)

= 2026