document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94894>Question 94894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 31.  Twice the lesser number is 6 less than twice the greater number.  What are 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 #69433 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=69433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L represent the lesser number and G represent the Greater.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The sum of these two numbers equals 31. In equation form this is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L + G = 31 <=== remember this first equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Twice the lesser number (L) plus 6 equals twice the greater number (G). In equation form<BR>\n" );
document.write( "this is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2L + 6 = 2G <=== this is the second equation<BR>\n" );
document.write( ".<BR>\n" );
document.write( "From the first equation we can solve for L by subtracting G from both sides. When you subtract<BR>\n" );
document.write( "G from both sides of the first equation the result is given by:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L = 31 - G<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In the second equation you can substitute 31 - G in place of L. The second equation then<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2(31 - G) + 6 = 2G<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Do the distributed multiplication on the left side by multiplying 2 times 31 and 2 times -G<BR>\n" );
document.write( "to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "62 - 2G + 6 = 2G<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the -2G on the left side by adding 2G to both sides. When you do that the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "62 + 6 = 4G<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Add the two numbers on the left side:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "68 = 4G<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for G by dividing both sides of this equation by 4 (the multiplier of G) and get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "68/4 = G<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Dividing 68 by 4 results in 17 and the equation is then:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "G = 17<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We now know that the greater number is 17, and since the two numbers add to 31, the lesser<BR>\n" );
document.write( "number L must be 31 - 17 = 14.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the two numbers are 17 and 14<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check: twice the lesser number is 2 times 14 or 28. Is this 6 less than twice the greater<BR>\n" );
document.write( "number or 2 times 17 = 34. Yes, 28 is 6 less than 34. Our answers check. The two numbers are<BR>\n" );
document.write( "14 and 17.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );