document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046349>Question 1046349</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Four cities lie along a straight highway in the order of city A B C and D.  the distance from city A to city B is five times the distance from city B to city CD. The distance from city A to city D is two times  The distance from city A to city B the distance between cities C to D is 10 miles. What is the distance between city AB? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661877 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are typos in that question.<BR>\n" );
document.write( "I am guessing the question meant states:<BR>\n" );
document.write( "The distance from city A to city B is five times the distance from city B to city C.<BR>\n" );
document.write( "The distance from city A to city D is two times the distance from city A to city B.<BR>\n" );
document.write( "The distance between cities C to D is 10 miles.<BR>\n" );
document.write( " <BR>\n" );
document.write( "A SHORT WRITE UP:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=5BC ALIGN=MIDDLE  ALT=\"AB=5BC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=2AB ALIGN=MIDDLE  ALT=\"AD=2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=10 ALIGN=MIDDLE  ALT=\"CD=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=AB%2BBC%2BCD ALIGN=MIDDLE  ALT=\"AD=AB%2BBC%2BCD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2AB=AB%2BBC%2B10 ALIGN=MIDDLE  ALT=\"2AB=AB%2BBC%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%285BC%29=5BC%2BBC%2B10 ALIGN=MIDDLE  ALT=\"2%285BC%29=5BC%2BBC%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10BC=6BC%2B10 ALIGN=MIDDLE  ALT=\"10BC=6BC%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10BC-6BC=10BC=10 ALIGN=MIDDLE  ALT=\"10BC-6BC=10BC=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=10%2F4 ALIGN=MIDDLE  ALT=\"BC=10%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=2.5 ALIGN=MIDDLE  ALT=\"BC=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5BC=5%282.5%29 ALIGN=MIDDLE  ALT=\"5BC=5%282.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5BC=12.5 ALIGN=MIDDLE  ALT=\"5BC=12.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=12.5 ALIGN=MIDDLE  ALT=\"AB=12.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance between city A and city B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812.5miles%29 ALIGN=MIDDLE  ALT=\"highlight%2812.5miles%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A LONGER EXPLANATION, WITH A VARIABLE SO IT LOOKS MORE LIKE ALGEBRA:<BR>\n" );
document.write( "Let us define a variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the distance from city B to city C, in miles.<BR>\n" );
document.write( "(We could call it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is shorter).<BR>\n" );
document.write( "Since the distance from city A to city B is five times the distance from city B to city C,<BR>\n" );
document.write( "the distance from city A to city B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The distance from A to C must be the sum of the two distances listed above:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2Bx=6x ALIGN=MIDDLE  ALT=\"5x%2Bx=6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So far we have this picture:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C100%2C-1%2C29%2C-2%2C3%2C%0D%0Aline%28-1%2C0%2C29%2C0%29%2Cred%28circle%2812.5%2C0%2C0.2%29%29%2C%0D%0Ared%28circle%2815%2C0%2C0.2%29%29%2Cred%28circle%280%2C0%2C0.2%29%29%2C%0D%0Ared%28circle%2825%2C0%2C0.2%29%29%2Clocate%28-0.2%2C-0.2%2CA%29%2C%0D%0Alocate%2812.3%2C-0.2%2CB%29%2Clocate%2814.8%2C-0.2%2CC%29%2C%0D%0Alocate%2824.8%2C-0.2%2CD%29%2Clocate%285.8%2C0%2C5x%29%2C%0D%0Alocate%2813.5%2C0.15%2Cx%29%2Cred%28arrow%287.5%2C1%2C0%2C01%29%29%2C%0D%0Ared%28arrow%287.5%2C1%2C15%2C1%29%29%2Clocate%287.1%2C1%2C6x%29%2C%0D%0Alocate%2825.3%2C-1.2%2Chighway%29%2Carrow%2828.2%2C-1.7%2C28.2%2C0%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We also know that the distance from city A to city D is two times the distance from city A to city B.<BR>\n" );
document.write( "So, th2 distance from city A to city D is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%285x%29=10x ALIGN=MIDDLE  ALT=\"2%2A%285x%29=10x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and we know that the distance between cities C to D is 10 miles.<BR>\n" );
document.write( "Now, the picture looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C100%2C-1%2C29%2C-2%2C3%2C%0D%0Alocate%2825.3%2C-1.2%2Chighway%29%2Carrow%2828.2%2C-1.7%2C28.2%2C0%29%2C%0D%0Aline%28-1%2C0%2C29%2C0%29%2Cred%28circle%2812.5%2C0%2C0.2%29%29%2C%0D%0Ared%28circle%2815%2C0%2C0.2%29%29%2Cred%28circle%280%2C0%2C0.2%29%29%2C%0D%0Ared%28circle%2825%2C0%2C0.2%29%29%2Clocate%28-0.2%2C-0.2%2CA%29%2C%0D%0Alocate%2812.3%2C-0.2%2CB%29%2Clocate%2814.8%2C-0.2%2CC%29%2C%0D%0Alocate%2824.8%2C-0.2%2CD%29%2Clocate%285.8%2C0%2C5x%29%2C%0D%0Alocate%2813.5%2C0.15%2Cx%29%2Cred%28arrow%287.5%2C1%2C0%2C01%29%29%2C%0D%0Ared%28arrow%287.5%2C1%2C15%2C1%29%29%2Clocate%287.1%2C1%2C6x%29%2C%0D%0Alocate%2819.7%2C0%2C10%29%2C%0D%0Ared%28arrow%2812.5%2C2%2C0%2C2%29%29%2Cred%28arrow%2812.5%2C2%2C25%2C2%29%29%2C%0D%0Alocate%2812%2C2%2C10x%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Considering the distances shown by the arrows<BR>\n" );
document.write( "between A and C <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%29 ALIGN=MIDDLE  ALT=\"%286x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and a<BR>\n" );
document.write( "between A and D <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%29 ALIGN=MIDDLE  ALT=\"%2810x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the distance between C and D must be their difference<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B6x=4x ALIGN=MIDDLE  ALT=\"10x%2B6x=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now, we can represent the situation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C100%2C-1%2C29%2C-2%2C3%2C%0D%0Alocate%2825.3%2C-1.2%2Chighway%29%2Carrow%2828.2%2C-1.7%2C28.2%2C0%29%2C%0D%0Aline%28-1%2C0%2C29%2C0%29%2Cred%28circle%2812.5%2C0%2C0.2%29%29%2C%0D%0Ared%28circle%2815%2C0%2C0.2%29%29%2Cred%28circle%280%2C0%2C0.2%29%29%2C%0D%0Ared%28circle%2825%2C0%2C0.2%29%29%2Clocate%28-0.2%2C-0.2%2CA%29%2C%0D%0Alocate%2812.3%2C-0.2%2CB%29%2Clocate%2814.8%2C-0.2%2CC%29%2C%0D%0Alocate%2824.8%2C-0.2%2CD%29%2Clocate%285.8%2C0%2C5x%29%2C%0D%0Alocate%2813.5%2C0.15%2Cx%29%2Cred%28arrow%287.5%2C1%2C0%2C01%29%29%2C%0D%0Ared%28arrow%287.5%2C1%2C15%2C1%29%29%2Clocate%287.1%2C1%2C6x%29%2C%0D%0Alocate%2819.7%2C0%2C10%29%2C%0D%0Ared%28arrow%2812.5%2C2%2C0%2C2%29%29%2Cred%28arrow%2812.5%2C2%2C25%2C2%29%29%2C%0D%0Alocate%2812%2C2%2C10x%29%2C%0D%0Agreen%28arrow%2820%2C1%2C15%2C1%29%29%2Cgreen%28arrow%2820%2C1%2C25%2C1%29%29%2C%0D%0Alocate%2818%2C1%2C10x-6x=4x%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Finally since the distance, in miles, between C and D is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=10 ALIGN=MIDDLE  ALT=\"4x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10%2F4 ALIGN=MIDDLE  ALT=\"x=10%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance, in miles, between B and C,<BR>\n" );
document.write( "and the distance, in miles, between A and B is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=5%2A2.5 ALIGN=MIDDLE  ALT=\"5x=5%2A2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=highlight%2812.5%29 ALIGN=MIDDLE  ALT=\"5x=highlight%2812.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The distance between city A and city B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812.5miles%29 ALIGN=MIDDLE  ALT=\"highlight%2812.5miles%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );