Question

According to projections through the year 2030, the population y of the given state in year x is approximated by

State A: - 5x+y=11,400
State B: -143x +y = 9,000
where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?

Answer 1

In the year 2026 population of both the states will be the 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, an 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 = 25.19 [After 25 years ]

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

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

= 2026