document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203234>Question 1203234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let x represent the smaller number and y the larger number. The sum of the two numbers is 200. If the larger number is 8 less than triple the smaller number, what are the two numbers?\r<BR>\n" );
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document.write( "The sum of two numbers is 200.    But I’m confused as to write if the larger number is 8 less than triple the<BR>\n" );
document.write( "X=200-y -> x=200-178.05             smaller #<BR>\n" );
document.write( "X=-y+200                                                                                <BR>\n" );
document.write( "Replace y with 178.05<BR>\n" );
document.write( "X=-178.05+200<BR>\n" );
document.write( "X=21.95<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838635 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You are told to let x be the smaller number and y be the larger number.  Then...<br><BR>\n" );
document.write( "(1) The sum of the two numbers is 200<BR>\n" );
document.write( "x+y=200<BR>\n" );
document.write( "You wrote x=-y+200<BR>\n" );
document.write( "That is equivalent to the basic equation, but harder to work with.  Leave the equation exactly as the words in the problem give it to you.<br><BR>\n" );
document.write( "(2) The larger number is 8 less than triple the smaller number<br><BR>\n" );
document.write( "It appears that you wrote an equation using the number 178.05.  Where did that number come from?  Maybe your work on paper is messy like mine usually is, and that number sneaked in from a different problem....<br><BR>\n" );
document.write( "Translating that given information into algebraic language is a crucial skill.  Take it a little bit at a time:<BR>\n" );
document.write( "the smaller number: x<BR>\n" );
document.write( "triple the smaller number: 3x<BR>\n" );
document.write( "8 less than triple the smaller number: 3x-8<br><BR>\n" );
document.write( "The larger number is 8 less than triple the smaller number: y=3x-8<br><BR>\n" );
document.write( "Note many beginning students go in the wrong direction here by trying to translate word for word into algebraic language, ending up with \"y=8-3x\".  But you have to listen to the whole phrase; 8 less than triple the smaller number means the \"8\" is subtracted from \"triple the smaller number\".<br><BR>\n" );
document.write( "So from (1) and (2) we have the system of equations<BR>\n" );
document.write( "x+y=200<BR>\n" );
document.write( "y=3x-8<br><BR>\n" );
document.write( "With the two equations in those forms, they are perfectly set up for solving by substitution; substitute \"3x-8\" for \"y\" in the first equation and go from there, as tutor @ikleyn does.<br><BR>\n" );
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