document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182379>Question 182379</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780131868465/algebrahomeworkh>aLGEBRA A COMBINED APPROACH</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\">  45 INCH BOARD IS TO BE CUT INTO THREE PIECES SO THAT THE SECOND PIECE IS 3 TIMES AS LONG AS THE FIRST PIECE AND THE THIRD PIECE IS 5 TIMES AS LONG AS THE FIRST PIECE. IF X REPRESENTS THE LENGTH OF THE FIRST PIECE, FIND THE LENGTHS OF ALL THREE PIECES </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136988 by </B><A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><B>MathGuyJoe(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><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=136988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First off, try to avoid typing in all caps -- it's difficult to read and some folks treat it as shouting.<BR>\n" );
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document.write( "Let x = length of 1st piece<BR>\n" );
document.write( "Let y = length of 2nd piece<BR>\n" );
document.write( "Let z = length of 3rd piece<BR>\n" );
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document.write( "We know the total length of the board is 45, so:<BR>\n" );
document.write( "<u>Equation 1:</u> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+%2B+z+=+45+ ALIGN=MIDDLE  ALT=\"+x+%2B+y+%2B+z+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We also know that the 2nd piece is 3 times the length of the 1st piece:<BR>\n" );
document.write( "<u>Equation 2:</u> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+ ALIGN=MIDDLE  ALT=\"+y+=+3x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We also know that he 3rd piece is 5 times the length of the 1st piece:<BR>\n" );
document.write( "<u>Equation 3:</u>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+5x+ ALIGN=MIDDLE  ALT=\"+z+=+5x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can substitute the values from equations 2 and 3 into equation 1:<BR>\n" );
document.write( "Equation 1:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+%2B+z+=+45+ ALIGN=MIDDLE  ALT=\"+x+%2B+y+%2B+z+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+%283x%29+%2B+%285x%29+=+45+ ALIGN=MIDDLE  ALT=\"+x+%2B+%283x%29+%2B+%285x%29+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving for x gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x+=+45+ ALIGN=MIDDLE  ALT=\"+9x+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++x+=+5+ ALIGN=MIDDLE  ALT=\"++x+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting this value back into equations 2 and 3 will give us the values of y and z:<BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3x+ ALIGN=MIDDLE  ALT=\"+y+=+3x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3%285%29+ ALIGN=MIDDLE  ALT=\"+y+=+3%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+15+ ALIGN=MIDDLE  ALT=\"+y+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Equation 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+5x+ ALIGN=MIDDLE  ALT=\"+z+=+5x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+5%285%29+ ALIGN=MIDDLE  ALT=\"+z+=+5%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+25+ ALIGN=MIDDLE  ALT=\"+z+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the final answers are <b>x = 5</b>, <b>y = 15</b> and <b>z = 25</b>. </SPAN>\n" );
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