document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104718>Question 104718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have been struggling all morning with a problem.  Here it is:<BR>\n" );
document.write( "The length of a rectangle is 1 less than twice its width.  If the width is 3 more than one-seventh of the perimeter, find the dimensions of the rectangle.  \r<BR>\n" );
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document.write( "While I can come up with a value for P which is a term, not a value, I cannot come up with any actual dimensions, and my answer will not proof out.  I have approached the problem different ways, such as width=x and length=2x+1 (using the 2L = 2S = P standard equation for finding perimeter), and w=1/7 P - 3, etc. for length, but I cannot come up with an actual answer.  Thanks in advance.\r<BR>\n" );
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document.write( "Maddie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76219 by </B><A HREF=/tutors/aboutme.mpl?userid=doukungfoo><B>doukungfoo(195)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=doukungfoo><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=doukungfoo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Perimeter of a rectangle is equal to the sum of its four sides.<BR>\n" );
document.write( "A rectangle has two sides that represent its length and<BR>\n" );
document.write( "two sides that represent its width. So <BR>\n" );
document.write( "perimeter = 2 times length plus 2 times width<BR>\n" );
document.write( "P = 2L + 2W<BR>\n" );
document.write( "Now for this rectangle we are told that the<BR>\n" );
document.write( "length = 2 times width minus 1<BR>\n" );
document.write( "L = 2W - 1<BR>\n" );
document.write( "We are also told that the <BR>\n" );
document.write( "width = 1/7 perimeter plus 3<BR>\n" );
document.write( "W = 1/7(P) + 3<BR>\n" );
document.write( "W = P/7 + 3<BR>\n" );
document.write( "Ok lets go back to the original equation for perimeter<BR>\n" );
document.write( "P = 2L + 2W<BR>\n" );
document.write( "since we have shown that L = 2W - 1 we can substitute 2W - 1 for L in<BR>\n" );
document.write( "P = 2L + 2W<BR>\n" );
document.write( "P = 2(2W-1) + 2W<BR>\n" );
document.write( "Now if we use this equation with W = P/7 +3 we have a system of equations in two varibles that we can solve for.<BR>\n" );
document.write( "So here are the two equations we will be working with:<BR>\n" );
document.write( "P = 2(2W-1) + 2W<BR>\n" );
document.write( "AND<BR>\n" );
document.write( "W = P/7 + 3<BR>\n" );
document.write( "Lets solve the system of equations using the substitution method.<BR>\n" );
document.write( "Since W = P/7 + 3 we can substitute P/7 + 3 for the W in <BR>\n" );
document.write( "P = 2(2W-1) + 2W<BR>\n" );
document.write( "P = 2(2(P/7 + 3)-1) + 2(P/7 + 3)<BR>\n" );
document.write( "Now we have and equation with just one variable to solve for<BR>\n" );
document.write( "P = 2(2(P/7 + 3)-1) + 2(P/7 + 3)<BR>\n" );
document.write( "P = 2(2P/7 + 6 - 1) + 2P/7 + 6<BR>\n" );
document.write( "P = 4P/7 + 12 - 2 + 2P/7 + 6<BR>\n" );
document.write( "P = 6P/7 + 16<BR>\n" );
document.write( "P = 6P/7 + 112/7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+%286P%2B112%29%2F7 ALIGN=MIDDLE  ALT=\"P+=+%286P%2B112%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7P = 6P + 112<BR>\n" );
document.write( "P = 112<BR>\n" );
document.write( "<B>The perimeter is 112</B><BR>\n" );
document.write( "use this to find the width<BR>\n" );
document.write( "W = P/7 + 3<BR>\n" );
document.write( "W = 112/7 + 3<BR>\n" );
document.write( "W = 16 + 3<BR>\n" );
document.write( "W = 19<BR>\n" );
document.write( "<B>The width of the rectangle is 19</B><BR>\n" );
document.write( "use this to find the length<BR>\n" );
document.write( "L = 2W - 1<BR>\n" );
document.write( "L = 2(19) - 1<BR>\n" );
document.write( "L = 38 - 1<BR>\n" );
document.write( "L = 37<BR>\n" );
document.write( "<B>The length of the rectangle is 37</B><BR>\n" );
document.write( "check answers with formula for perimeter<BR>\n" );
document.write( "P = 2L + 2W<BR>\n" );
document.write( "112 = 2(37) + 2(19)<BR>\n" );
document.write( "112 = 74 + 38<BR>\n" );
document.write( "112 = 112\r<BR>\n" );
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document.write( " </SPAN>\n" );
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