document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196779>Question 1196779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Susan Hansen Group in St. George, Utah, sells $16,000,000 of single-family homes and townhomes a year. Assume single-family homes, with an average selling price of $260,000, sell 1.5 times more often than townhomes, with an average selling price of $230,000. How many of each are sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829768 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "\"1.5 times MORE often\" means 2.5 times AS OFTEN.  It's the same as an increase of 150% meaning the new number is 250% of the original.<br><BR>\n" );
document.write( "Using that (and working in thousands of dollars)....<br><BR>\n" );
document.write( "x = # of townhomes<BR>\n" );
document.write( "2.5x = # of single-family homes<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=230%28x%29%2B260%282.5x%29=16000 ALIGN=MIDDLE  ALT=\"230%28x%29%2B260%282.5x%29=16000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=230x%2B650x=16000 ALIGN=MIDDLE  ALT=\"230x%2B650x=16000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=880x=16000 ALIGN=MIDDLE  ALT=\"880x=16000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "....<br><BR>\n" );
document.write( "We still don't get an integer answer....<br><BR>\n" );
document.write( "So, regardless of whether the \"1.5 times more often\" is (wrongly) interpreted as meaning 1.5 times AS often, or is interpreted correctly as 2.5 times as often, the given information is faulty.<br><BR>\n" );
document.write( "That's pretty sad.  Usually, when a problem uses a phrase like \"1.5 times as often\" or \"3 times more than\", only one of the two interpretations yields an integer answer, giving an indication of what the author of the problem really meant.<br><BR>\n" );
document.write( "But in this case neither interpretation gives a valid answer.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );