document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550023>Question 550023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference between two numbers is 10.When eight times the smaller number is added to 40, the result i ten less than three times 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 #358330 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=358330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x and y be the numbers.  You can use any letters. \r<BR>\n" );
document.write( "\n" );
document.write( "Let x = larger number\r<BR>\n" );
document.write( "\n" );
document.write( "Let y = smaller number\r<BR>\n" );
document.write( "\n" );
document.write( "x - y = 10<BR>\n" );
document.write( "8x + 40 = 3y - 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have a system if linear equations in two variables.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I will solve x - y = 10 for x and plug the answer into the other equation to find y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x - y = 10\r<BR>\n" );
document.write( "\n" );
document.write( "x = y + 10\r<BR>\n" );
document.write( "\n" );
document.write( "8(y + 10) + 40 = 3y - 10\r<BR>\n" );
document.write( "\n" );
document.write( "8y + 80 + 40 = 3y - 10\r<BR>\n" );
document.write( "\n" );
document.write( "8y + 120 = 3y - 10\r<BR>\n" );
document.write( "\n" );
document.write( "8y - 3y = -120 - 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5y = -130\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = -130/5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = -26\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To solve for x, replace y with -26 in either of the two equations above and simplify.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I will use x - y = 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let y = -26\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x - (-26) = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 26 = 10\r<BR>\n" );
document.write( "\n" );
document.write( "x = 10 - 26\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = -16\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The smaller number is -26 and the bigger number is -16.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The number -16 is BIGGER than -26 because it is closer to zero on the real number line.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );