SOLUTION: Given that -4 ≤ x ≤ -2 and 2 ≤ y ≤ 4, what is the largest possible value of (x+y)/x?

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Question 1148538: Given that -4 ≤ x ≤ -2 and 2 ≤ y ≤ 4, what is the largest possible value of (x+y)/x?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

            This problem is  VERY  SIMPLE.

            Moreover, it is  EXTREMELY  SIMPLE,  and I will show it to you right now. 


Our function is   = 1 + .      (1)


The given area is the square  ABCD  in quadrant  QII  with the vertices  

A= (-4,2),  B= (-2,2),  C= (-2,4),  D= (-4,4).



The given function, OBVIOUSLY, adds the ratio    to the value of 1.


But this ratio    is negative in QII.


Thus the function (1), actually, adds NEGATIVE amount to 1.



    - When the function (1) will have the largest value ?

    - OBVIOUSLY, when this negative addend    will have minimal absolute value.



        - When this addend    will have minimal absolute value ?

        - OBVIOUSLY,  when positive "y" is minimal and negative "x" has maximal absolute value.



             - Now, what is the point of the given square, where positive "y" is minimal and negative "x" has maximal absolute value ?

             - OBVIOUSLY, this point is  A= (-4,2).



Then the larges possible value of  the function     is    =  = 1 -  = .    ANSWER

Solved, explained, answered and completed.



/\/\/\/\/\/\/\/

O-o-o, tutor @greenestamps successfully retold my solution to this problem !

Congratulations (!) (!)

It seems, you invented the new way to increase the number of your posts by retelling my solutions !



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Rewrite the given expression as .

The allowable x values are all negative, and the allowable y values are all positive; that means y/x is negative.

Since we want the value of the expression to be as large as possible, we want to subtract the smallest amount we can. That means we want the absolute value of the numerator to be as small as possible and the absolute value of the denominator to be as large as possible.

So we choose y=2 and x=-4; and the largest possible value we can get for the expression is



-----------------------------------------------------------
to tutor @ikleyn...

why, oh why, do you have to be so thin-skinned when another tutor posts a solution that is similar to yours?

The purpose of my post was not to increase my number of posts by re-telling your solution.

In your post, you start out by saying that the solution is simple -- and then you introduce the totally unnecessary picture of a rectangle in the coordinate plane defining the specified x- and y-values.

My post was made to provide a solution that was simpler than your "simple" solution.

GROW UP!
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