Question 1177662
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        As the problem is solved in the post by @CPhill, it is one of possible ways/methods,

        but there is another, much more effective and more impressive way to solve the problem 

        using only one equation from the very beginning, instead of three.


        Also, it is worth to notice one very important fact:

        in the problem the information about  4  companies is given,  but actually only three 

        companies participate in the game.  The fourth company,  Jet Blue,  is introduced

        and does present only to confuse the reader and to distract attention.



<pre>
Let x be the number of empty seats for American.

Then the number of empty seats for United Continental is 3x,
and the number of empty seats for Southwest is (235 - x - 3x) = 235 - 4x.


Now write the total cost equation for empty seats

    United Cont.        American        Southwest
    3000*0.149*(3x)  +  3000*0.146*x  + 3000*0.124*(235-4x) = 99060  dollars.


Simplify and find x

     1341x            + 438x          + 87420 - 1488x  = 99060

                        291x                           = 99060 - 87420 = 11640.

                           x                           = 11640/191 = 40.


So, the number of empty seats for American is 40;  for United Continental  3*40 = 120,
                          and for Southwest 235-4*40 = 75.
</pre>

Solved.


Notice that in this solution the system of three equations is not even mentioned.