document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=670937>Question 670937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a 8 ft board is to be cut into three pieces, two equal length ones and the third 3 in shorter than the other two. If the cutting does not result in any length being lost, how long are the pieces? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #417223 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the 3d length has to be less than the other 2.<BR>\n" );
document.write( "this means that the maximum length of the 3d piece has to less than 8/3 feet.<BR>\n" );
document.write( "if we're assuming that there has to be something left over, then the minimum length of the 3d piece has to be greater than 0.<BR>\n" );
document.write( "so we have a minimum length of the 3d piece of greater than 0 and a maximum length of the 3d piece of smaller than 8/3.<BR>\n" );
document.write( "anything in between should be ok.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "let the 3d piece be equal to 1 foot.<BR>\n" );
document.write( "this means the 2 other pieces are 7/2 feet each.<BR>\n" );
document.write( "let the 3d piece be equal to 2 feet.<BR>\n" );
document.write( "this means the 2 other pieces at 6/2 feet each.<BR>\n" );
document.write( "as long as you don't need to have integers, there are an infinite number of lengths that would satisfy the requirements.<BR>\n" );
document.write( "if you assume some discrete amount, like no length could have an measurement that doesn't end in an inch, then  you now have a finite number of possible solutions.<BR>\n" );
document.write( "in fact, this probably means that the 3d piece needs to be in 2 inch increments which will allow the 2 equal pieces to be in 1 inch increments.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "3d piece equals 1 foot which means the 2 equal pieces equal 7/2 = 3.5 feet each.<BR>\n" );
document.write( "3.5 is  equivalent to 3 and 6 inches which is in increments of an inch so we're good.<BR>\n" );
document.write( "if we increase 3d section to 1foot 1 inch then we have 6 feet 11 inches left which we divide by 2 to get 3 feet 5.5 inches which is less than inch increments so we're not good.<BR>\n" );
document.write( "we would need to increase 3d section to 1 foot 2 inches (increments of 2 inches) to get 1 inch increments on the equal segments.<BR>\n" );
document.write( "1 foot 2 inches from 8 feet leaves 6 feet 10 inches which divided by 2 equals 3 feet 5 inches for each of the equal segments.<BR>\n" );
document.write( "not exactly sure what you were looking for but this is the solution based on my understanding of what you are asking.\r<BR>\n" );
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