document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114013>Question 114013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three times the sum of two numbers exceeds twice their difference by five, while half the sum is two more than the difference. what are the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83037 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be x & y<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Three times the sum of two numbers exceeds twice their difference by five,<BR>\n" );
document.write( "3(x+y) = 2(x-y) + 5<BR>\n" );
document.write( "Arrange equation in the standard form<BR>\n" );
document.write( "3x + 3y = 2x - 2y + 5<BR>\n" );
document.write( "3x - 2x + 3y + 2y = 5<BR>\n" );
document.write( "x + 5y = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"while half the sum is two more than the difference.\"<BR>\n" );
document.write( ".5(x+y) = x - y  + 2<BR>\n" );
document.write( "Get rid of the decimal, multiply by 2<BR>\n" );
document.write( "x + y = 2x - 2y + 4<BR>\n" );
document.write( "x - 2x + y + 2y = 4<BR>\n" );
document.write( "-x + 3y = 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can solve this by elimination:<BR>\n" );
document.write( "x + 5y = 5<BR>\n" );
document.write( "-x + 3y = 4<BR>\n" );
document.write( "-------------adding eliminates x, find y<BR>\n" );
document.write( "8y = 9<BR>\n" );
document.write( "y = 9/8<BR>\n" );
document.write( "y = 1.125<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find x using x + 5y = 5:<BR>\n" );
document.write( "x + 5(1.125) = 5<BR>\n" );
document.write( "x + 5.625 = 5<BR>\n" );
document.write( "x = 5 - 5.625<BR>\n" );
document.write( "x = -.625<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Two non-integer solutions. See if they satisfy the original statement equations<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3(x+y) = 2(x-y) + 5<BR>\n" );
document.write( "3(-.625 + 1.125) = 2(-.625 - 1.125) + 5<BR>\n" );
document.write( "3(.5) = 2(-1.75) + 5<BR>\n" );
document.write( "1.5 = -3.5 + 5<BR>\n" );
document.write( "1.5 = 1.5 Confirms our solution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check our solutions in:<BR>\n" );
document.write( ".5(x+y) = x - y + 2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );