document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242805>Question 242805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is eleven more than twice another. If their sum is decreased by nine, the result is seventeen. 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 #177776 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=177776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the setup to the problem, always try to minimize the unknowns.<BR>\n" );
document.write( "x = one number<BR>\n" );
document.write( "It is 11 more than twice another number.<BR>\n" );
document.write( "y = another number<BR>\n" );
document.write( "x = 2y + 11<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Now the second part says if the sum of x + y is decreased by 9 (that is:  x + y - 9), the result is 17.<BR>\n" );
document.write( "x + y - 9 = 17<BR>\n" );
document.write( "Add 9 to both sides<BR>\n" );
document.write( "x + y = 17+9 = 26<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Now we have to solve x and y<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Subtracting y from both sides of the equation above.<BR>\n" );
document.write( "x + y - y = 26 - y<BR>\n" );
document.write( "x = 26 - y<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Substituting in the other equation.<BR>\n" );
document.write( "x = 2y + 11<BR>\n" );
document.write( "26 - y = 2y + 11<BR>\n" );
document.write( "Adding y to both sides<BR>\n" );
document.write( "26 = 3y + 11<BR>\n" );
document.write( "Subtracting 11 from both sides<BR>\n" );
document.write( "15 = 3y<BR>\n" );
document.write( "Dividing both sides by 3<BR>\n" );
document.write( "5 = y<BR>\n" );
document.write( "...<BR>\n" );
document.write( "y = 5<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Recall<BR>\n" );
document.write( "x + y = 26<BR>\n" );
document.write( "Substituting for y<BR>\n" );
document.write( "x + 5 = 26<BR>\n" );
document.write( "Subtracting 5 from both sides<BR>\n" );
document.write( "x = 21<BR>\n" );
document.write( "Check your work (even if you're tired)...<BR>\n" );
document.write( "Does x = 2y + 11?<BR>\n" );
document.write( "21 = 2(5) + 11?<BR>\n" );
document.write( "Yes it does.<BR>\n" );
document.write( "Does x + y - 9 = 17?<BR>\n" );
document.write( "21 + 5 - 9 = 17?<BR>\n" );
document.write( "Yes it does.<BR>\n" );
document.write( "So we're done.<BR>\n" );
document.write( "x = 21<BR>\n" );
document.write( "y = 5 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );