On the basis of data from 1990 to 2006, the median income y in the year x for men and women is approximated by the equations given below, where x=0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, in what year will the median income of men and women be the same? Men: -236x + 2y = 56,939 Women: -838x + 3y = 41,655

The median income would be the same, based on these equations, in approximately 90.4 years time, which is around approximately in the year 2080

Step-by-step explanation:

Given the approximate equations for men and women respectively:

Where X stands for number of years and y stands for median. Since we are looking for the year, x, where the median, y, would be the same, then we have to rewrite both equations such that y would be the subject of the equations, why? So that, we can have an equation for the median income, and whenever the median income becomes equal, we would have a certain number years, X, that would happen, here is what I'm trying to say:

The first equation can be rewritten as:

Dividing both sides by 2, we have:

Similarly, from the second equation we have:

Dividing both sides by 3, we have:

Now, we have the equations in terms of y, from both equations we can say:

We have to solve for x, the number of years, in order to get when y, the median would be equal.

Multiply both sides of the last equation by 6 we get:

Which gives:

Collecting like terms we have:

We then have:

Dividing both sides of the last equation by 968

We get:

(approximately)

Therefore the number years we need for the median income to be the same is approximately 90.4years which will fall around 2080. And that is the required answer.