document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045390>Question 1045390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number added to thrice its reciprocal is equal to 13/2. what is the number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660819 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=660819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is nothing that says that the number is a positive integer,<BR>\n" );
document.write( "but if that had been meant,the fifth grader approach would work well.<BR>\n" );
document.write( "Otherwise, we could use the algebra approach.<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE FIFTH GRADER APPROACH:<BR>\n" );
document.write( "It cannot be a very small number, like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because the sum would be too low.<BR>\n" );
document.write( "It cannot be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or more,<BR>\n" );
document.write( "because the sum would be more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=14%2F2%3E13%2F2 ALIGN=MIDDLE  ALT=\"7=14%2F2%3E13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It must be a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because the sum has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator.<BR>\n" );
document.write( "Could the number be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "Its reciprocal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the sum i<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B3%281%2F4%29=4%2B3%2F4=16%2F4%2B3%2F4=19%2F4 ALIGN=MIDDLE  ALT=\"4%2B3%281%2F4%29=4%2B3%2F4=16%2F4%2B3%2F4=19%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2=26%2F4 ALIGN=MIDDLE  ALT=\"13%2F2=26%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The sum is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and obviously the bigger the starting number,<BR>\n" );
document.write( "the larger the sum will be,<BR>\n" );
document.write( "so let's try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the sum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus thrice its reciprocal is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B3%281%2F6%29=6%2B3%2F6=6%2B1%2F2=12%2F2%2B1%2F2=13%2F2 ALIGN=MIDDLE  ALT=\"6%2B3%281%2F6%29=6%2B3%2F6=6%2B1%2F2=12%2F2%2B1%2F2=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%286%29 ALIGN=MIDDLE  ALT=\"highlight%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE ALGEBRA APPROACH:<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 mystery number, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = its reciprocal, so we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%281%2Fx%29 ALIGN=MIDDLE  ALT=\"x%2B3%281%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the mystery number added to thrice its reciprocal.<BR>\n" );
document.write( "The problem say that sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so our equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%281%2Fx%29=13%2F2 ALIGN=MIDDLE  ALT=\"x%2B3%281%2Fx%29=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%281%2Fx%29=13%2F2 ALIGN=MIDDLE  ALT=\"x%2B3%281%2Fx%29=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Fx=13%2F2 ALIGN=MIDDLE  ALT=\"x%2B3%2Fx=13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We multiply both sides of the equal sign in that equation times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since we now that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we know we get an equivalent equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2Fx%29%2A2x%29=%2813%2F2%29%2A2x ALIGN=MIDDLE  ALT=\"%28x%2B3%2Fx%29%2A2x%29=%2813%2F2%29%2A2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B%283%2Fx%29%2A2x=13x ALIGN=MIDDLE  ALT=\"2x%5E2%2B%283%2Fx%29%2A2x=13x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B6=13x ALIGN=MIDDLE  ALT=\"2x%5E2%2B6=13x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-13x%2B6=0 ALIGN=MIDDLE  ALT=\"2x%5E2-13x%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can solve that equation by factoring,<BR>\n" );
document.write( "by completing the square,<BR>\n" );
document.write( "or by using the quadratic formula,<BR>\n" );
document.write( "to get the solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );