Question 899640
This is Uniform Rates for fuel efficiency.
R = fuel efficiency
V = volume of fuel in gallons
D = distance in miles
RV=D


A data table might help.


___________________rate_________volume__________distance
CITY________________27
HIWAY_______________38
TOTALS___________________________36______________1192


Use the basic equation to help fill the missing volume and distance data; assign variables, either for the volumes, or the distances.  In fact, you could assign variables just to either the City or to the Highway.  



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ASSIGNING VARIABLES <s>DIFFERENTLY</s>
-
___________________rate_________volume__________distance
CITY________________27___________c/27_______________c
HIWAY_______________38___________h/38_______________h
TOTALS___________________________36______________1192


Form two equations.
-
{{{c/27+h/38=36}}}
LCD=2*2*3*3*3*19
{{{76c+54h=73872}}}
-
{{{c+h=1192}}}
-
{{{highlight_green(system(76c+54h=73872,c+h=1192))}}}
Multiply the c+h equation by 54, subtract from the 76c+54h equation.
{{{76c+54h-(54c+54h)=73872-54*1192}}}
{{{22c=9504}}}
{{{c=9504/22}}}
{{{highlight(highlight(c=432))}}}, miles of city driving.




-----------THIS ATTEMPT HAS UNKNOWN MISTAKE--------
This attempt will be to JUST assign c = distance done for the city.
The reason is that the question asks specifically for this.


___________________rate_________volume____________________distance
CITY________________27___________c/27_______________________c
HIWAY_______________38__________(1192-c)/38_________________1192-c
TOTALS___________________________36_________________________1192


That single variable assigning appears to be workable for a solution.  The equation to solve will be {{{highlight_green(c/27+(1192-c)/38=36)}}}.


The denominators are a bit inconvenient.  
3*3*3, 2*19, 2*2*3*3
Lowest Common Denominator is {{{highlight_green(2*2*3*3*3*19)}}}, and most easily used in this factored form. Multiply left and right members by this.


{{{4*19*c+(1192-c)*3*3*3*2=3*19}}}
{{{76c+54*1192-54c=57}}}
22c---------------------------------AND THE SOLUTION IS FAILING BECAUSE MAKES A NEGATIVE VALUE FOR c