document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38255>Question 38255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tweeledum says \"the sum of your weight and twice mine is 361 pounds.\" Tweedledee says \"Contrariwiwse, the sum of your weight and twice mine is 362 pounds.\" if they are both correct, how much do Tweedledum and Tweedledee weight together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23741 by </B><A HREF=/tutors/aboutme.mpl?userid=junior403><B>junior403(76)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=junior403><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=23741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To make it easier lets write this equation in terms of x and y...<BR>\n" );
document.write( "Tweeledum (y) says \"the sum of your weight (x) and (+) twice mine (2y) is (=) 361 pounds.\" <BR>\n" );
document.write( "x + 2y = 361<BR>\n" );
document.write( "Tweedledee (x) says \"Contrariwiwse, the sum of your weight (y) and (+) twice mine (2x) is (=) 362 pounds.\" <BR>\n" );
document.write( "2x + y = 362<BR>\n" );
document.write( "If they are both correct, how much do Tweedledum and Tweedledee weight together?<BR>\n" );
document.write( "This word problem is best solved by using a \"system of equations\"<BR>\n" );
document.write( "Here's how...<BR>\n" );
document.write( "We take our two statements we just made and \"stack\" them on top of each other...<BR>\n" );
document.write( "x + 2y = 361<BR>\n" );
document.write( "2x + y = 362<BR>\n" );
document.write( "We have two variables we are working with. We need to figure out the value of one before we can identify the value of the other. So lets solve one equation for x first using the substitution method for solving systems of equations.<BR>\n" );
document.write( "x + 2y = 361 (solve for x)<BR>\n" );
document.write( "Subtract 2y from both sides...<BR>\n" );
document.write( "x = 361 - 2y<BR>\n" );
document.write( "Now (361 - 2y) is our value for x.<BR>\n" );
document.write( "So we now insert the value for x into the other equation...<BR>\n" );
document.write( "2(361 - 2y) + y = 362<BR>\n" );
document.write( "Now we distribute...<BR>\n" );
document.write( "722 - 4y + y = 362<BR>\n" );
document.write( "Subtract 722 from both sides to isolate the variable...<BR>\n" );
document.write( "-4y + y = -360<BR>\n" );
document.write( "Combine like terms...<BR>\n" );
document.write( "-3y = -360<BR>\n" );
document.write( "Now divide both sides by -3...<BR>\n" );
document.write( "y = 120 (this is the weight of tweedledee)<BR>\n" );
document.write( "Now to find the weight of the other we need to take our solution and substitute it for the value of y in the opposite equation...<BR>\n" );
document.write( "x + 2(120) = 361<BR>\n" );
document.write( "Now solve...<BR>\n" );
document.write( "x + 240 = 361<BR>\n" );
document.write( "Subtract 240 from each side...<BR>\n" );
document.write( "x = 121 ( this is the weight of tweedledum)<BR>\n" );
document.write( "To check we complete the equation with both solutions...<BR>\n" );
document.write( "121 + 2(120) = 361 <BR>\n" );
document.write( "121 + 240 = 361<BR>\n" );
document.write( "361 = 361<BR>\n" );
document.write( "Correct...<BR>\n" );
document.write( "2(121) + 120 = 362<BR>\n" );
document.write( "242 + 120 = 362<BR>\n" );
document.write( "362 = 362<BR>\n" );
document.write( "Correct...<BR>\n" );
document.write( "Tweedledee weighs 121 lbs.<BR>\n" );
document.write( "Tweedledum weighs 120 lbs.<BR>\n" );
document.write( "To answer the original question...<BR>\n" );
document.write( "121 + 120 = 241 lbs. together!<BR>\n" );
document.write( "I hope this helps!<BR>\n" );
document.write( "Good luck! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );