Question 1148436
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From the condition, Bob and Ted had initially  5x and 2x dollars, respectively.


Then each of them spent equal amount of "y" dollars.


After that, they  possessed  5x-y  and  2x-y dollars respectively, and  


    {{{(5x-y)/(2x-y)}}} = {{{6/1}}} = 6,

so

    5x-y = 6*(2x-y),

    5x - y = 12x - 6y

     5y = 7x.            (1)


Also, we are given that

    (5x-y) + (2x-y) = 126  dollars,   or


     7x - 2y = 126.      (2)


In (2), replace  7x  by  5y, based on (1).  You will get


    5y - 2y = 126,

    3y      = 126

     y      = 126/3 = 42.


Then from (1),  x = {{{(5y)/7}}} = {{{(5*42)/7}}} = 5*6 = 30.


<U>ANSWER</U>.  Initially, they had  5x + 2x = 7x = 7*30 = 210 dollars.   
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Solved.