document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628054>Question 628054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you Use an algebraic approach to solve the problem. \r<BR>\n" );
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document.write( "A board 45 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.\r<BR>\n" );
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document.write( "so far what i have is 2/3x=45 is this right? if so how do you solve? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395337 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=395337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let's see if your approach makes sense.  You said <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{3}x\ =\ 45\">.  If a part of the quantity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> is equal to 45, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> must be bigger than 45.   If I asked you for two-thirds of the money in your wallet and you handed me $45, you must have started with more than the 45 bucks, right?  That means, according to your theory, that one of the pieces of board is longer than the piece it was cut from.  Absurd in the extreme.\r<BR>\n" );
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document.write( "Read the problem carefully.  I'm going to assign <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> to represent the measure of the longer piece, just because it is easier to explain the problem that way.  Generally you will want to assign your variable to represent the quantity asked for by the problem, but that is just a little inconvenient this time.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> represent the measure of the longer piece.  Then we are given that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{3}x\"> is the measure of the shorter piece.  Together (except for a negligible saw kerf) the two boards should add up to the original 45 feet.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ \frac{2}{3}x\ =\ 45\">\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> and then calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{3}x\">\r<BR>\n" );
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document.write( "Step 1:  Multiply both sides by 3:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x\ +\ 2x\ =\ 105\">\r<BR>\n" );
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document.write( "Step 2:  Collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5x\ =\ 135\">\r<BR>\n" );
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document.write( "Step 3:  Multiply by the reciprocal of the coefficient on the variable:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{5}\,\cdot\,5x\ =\ \frac{1}{5}\,\cdot\,135\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 27\">\r<BR>\n" );
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document.write( "Which is the measure of the larger piece.  You can either calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{2}{3}\,\cdot\,27\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 45\ -\ 27\"> to find the measure of the shorter piece.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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