document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237192>Question 237192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is one-third of another number. The sum of the two numbers is 1 less than twice the larger number. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174960 by </B><A HREF=/tutors/aboutme.mpl?userid=College+Student><B>College Student(505)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=College+Student><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=College+Student><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we know one number is one third of another number, we can say:<BR>\n" );
document.write( "x = one number<BR>\n" );
document.write( "1/3x = the other number<BR>\n" );
document.write( "Now, we also know their sum equals the larger # minus 1, so here's your equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B%281%2F3%29x=x-1 ALIGN=MIDDLE  ALT=\"x%2B%281%2F3%29x=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve for x to find the first number:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x=x-1-x ALIGN=MIDDLE  ALT=\"%281%2F3%29x=x-1-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x=-1 ALIGN=MIDDLE  ALT=\"%281%2F3%29x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...multiply by 3 on both sides...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  This is your first number.<BR>\n" );
document.write( "Now calculate your second number by pluging this value in <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x ALIGN=MIDDLE  ALT=\"%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29-3 ALIGN=MIDDLE  ALT=\"%281%2F3%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  This is your second number.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Proof:<BR>\n" );
document.write( "Plug in these values in the original equation.  Both sides of the eqn must equal to each other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B%281%2F3%29x=x-1 ALIGN=MIDDLE  ALT=\"x%2B%281%2F3%29x=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...by substitution...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2B%28-1%29=%28-3%29-1 ALIGN=MIDDLE  ALT=\"-3%2B%28-1%29=%28-3%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=-4 ALIGN=MIDDLE  ALT=\"-4=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Done! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );