Respuesta :
Answer:
X=$195.78
Y=$51571.95
This will be the same in the year 2006
Step-by-step explanation:
-236x +2y =56939 ..eq1
-838x + 3y= 41655 ..eq2
Multiply eq1 by-3 and eq2 by 2 gives:
378x - 6y= -170817
-1676x +6y= 83310
Subtracting gives:
-1298x= -254127
Dividing with -1298
X= $195.78
Substituting the value of X in eq2
-236(195.78) + 2y= 56939
-46204.91 - 56939=-2y
103143.91/2=y
Y=$ 51571.95
Answer:
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:
[tex]-236x + 2y = 56 939[/tex]
[tex]-838x + 3y = 41 655[/tex]
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:
[tex]2y = 56 939 + 236x[/tex]
Dividing both sides by 2, we have:
[tex]y = \frac{1}{2}(56 939 + 236x)[/tex]
Similarly, from the second equation we have:
[tex]3y = 41 655 + 838x[/tex]
Dividing both sides by 3, we have:
[tex]y = \frac{1}{3}(41 655 + 838x)[/tex]
Now, we have the equations in terms of y, from both equations we can say:
[tex]\frac{1}{3}(41 655 + 838x) = \frac{1}{2}(56 939 + 236x)[/tex]
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:
[tex]2(41 655 + 838x) = 3(56 939 + 236x)[/tex]
Which gives:
[tex] 83 310 + 1 676x = 170 817 + 708x[/tex]
Collecting like terms we have:
[tex]1 676x - 708x = 170 817 - 83 310[/tex]
We then have:
[tex]968x = 87 507[/tex]
Dividing both sides of the last equation by 968
We get:
[tex]x = 90.4[/tex](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.
