document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=899640>Question 899640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A salesperson purchased an automobile that was advertised as averaging 27 mi/gal in the city and 38 mi/gal on the highway. A recent sales trip that covered 1192 miles required 36 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #545550 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=545550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is Uniform Rates for fuel efficiency.<BR>\n" );
document.write( "R = fuel efficiency<BR>\n" );
document.write( "V = volume of fuel in gallons<BR>\n" );
document.write( "D = distance in miles<BR>\n" );
document.write( "RV=D\r<BR>\n" );
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document.write( "A data table might help.\r<BR>\n" );
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document.write( "___________________rate_________volume__________distance<BR>\n" );
document.write( "CITY________________27<BR>\n" );
document.write( "HIWAY_______________38<BR>\n" );
document.write( "TOTALS___________________________36______________1192\r<BR>\n" );
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document.write( "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.  \r<BR>\n" );
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document.write( "ASSIGNING VARIABLES <s>DIFFERENTLY</s><BR>\n" );
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document.write( "___________________rate_________volume__________distance<BR>\n" );
document.write( "CITY________________27___________c/27_______________c<BR>\n" );
document.write( "HIWAY_______________38___________h/38_______________h<BR>\n" );
document.write( "TOTALS___________________________36______________1192\r<BR>\n" );
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document.write( "Form two equations.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2F27%2Bh%2F38=36 ALIGN=MIDDLE  ALT=\"c%2F27%2Bh%2F38=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "LCD=2*2*3*3*3*19<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76c%2B54h=73872 ALIGN=MIDDLE  ALT=\"76c%2B54h=73872\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Bh=1192 ALIGN=MIDDLE  ALT=\"c%2Bh=1192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28system%2876c%2B54h=73872%2Cc%2Bh=1192%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28system%2876c%2B54h=73872%2Cc%2Bh=1192%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply the c+h equation by 54, subtract from the 76c+54h equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76c%2B54h-%2854c%2B54h%29=73872-54%2A1192 ALIGN=MIDDLE  ALT=\"76c%2B54h-%2854c%2B54h%29=73872-54%2A1192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22c=9504 ALIGN=MIDDLE  ALT=\"22c=9504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=9504%2F22 ALIGN=MIDDLE  ALT=\"c=9504%2F22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28c=432%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28c=432%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, miles of city driving.\r<BR>\n" );
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document.write( "-----------THIS ATTEMPT HAS UNKNOWN MISTAKE--------<BR>\n" );
document.write( "This attempt will be to JUST assign c = distance done for the city.<BR>\n" );
document.write( "The reason is that the question asks specifically for this.\r<BR>\n" );
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document.write( "___________________rate_________volume____________________distance<BR>\n" );
document.write( "CITY________________27___________c/27_______________________c<BR>\n" );
document.write( "HIWAY_______________38__________(1192-c)/38_________________1192-c<BR>\n" );
document.write( "TOTALS___________________________36_________________________1192\r<BR>\n" );
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document.write( "That single variable assigning appears to be workable for a solution.  The equation to solve will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28c%2F27%2B%281192-c%29%2F38=36%29 ALIGN=MIDDLE  ALT=\"highlight_green%28c%2F27%2B%281192-c%29%2F38=36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The denominators are a bit inconvenient.  <BR>\n" );
document.write( "3*3*3, 2*19, 2*2*3*3<BR>\n" );
document.write( "Lowest Common Denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%282%2A2%2A3%2A3%2A3%2A19%29 ALIGN=MIDDLE  ALT=\"highlight_green%282%2A2%2A3%2A3%2A3%2A19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and most easily used in this factored form. Multiply left and right members by this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A19%2Ac%2B%281192-c%29%2A3%2A3%2A3%2A2=3%2A19 ALIGN=MIDDLE  ALT=\"4%2A19%2Ac%2B%281192-c%29%2A3%2A3%2A3%2A2=3%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=76c%2B54%2A1192-54c=57 ALIGN=MIDDLE  ALT=\"76c%2B54%2A1192-54c=57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "22c---------------------------------AND THE SOLUTION IS FAILING BECAUSE MAKES A NEGATIVE VALUE FOR c </SPAN>\n" );
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