document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199165>Question 1199165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Beth's garden is x - 2 feet wide and x +1 feet long. the total area is of the garden 10 square feet.    what is the length of the garden in feet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832876 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Assuming x is an integer, then here are the ways to multiply to 10 using only positive integers:<BR>\n" );
document.write( "1*10 = 10<BR>\n" );
document.write( "2*5 = 10\r<BR>\n" );
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document.write( "The gap from x-2 to x+1 is 3 units <BR>\n" );
document.write( "Since the gap from -2 to +1 is also 3 units.<BR>\n" );
document.write( "Use a number line to see this.\r<BR>\n" );
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document.write( "Because of this 3 unit gap, we ignore the factor pair 1*10.<BR>\n" );
document.write( "Instead we go for 2*5 which has the 3 unit gap.\r<BR>\n" );
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document.write( "x-2 is the smaller of the x expressions.<BR>\n" );
document.write( "Meaning the value of x-2 must be 2<BR>\n" );
document.write( "This means x+1 must be 5\r<BR>\n" );
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document.write( "Answer: The length of the garden is 5 feet long.\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "This is probably the more standard universal approach.\r<BR>\n" );
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document.write( "The width x-2 and length x+1 are multiplied to get the area of 10 sq ft.\r<BR>\n" );
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document.write( "width*length = area<BR>\n" );
document.write( "(x-2)*(x+1) = 10<BR>\n" );
document.write( "w(x+1) = 10 ...... let w = x-2<BR>\n" );
document.write( "wx+w = 10 ...... distribute<BR>\n" );
document.write( "x(w) + 1(w) = 10<BR>\n" );
document.write( "x(x-2) + 1(x-2) = 10 .... plug in w = x-2<BR>\n" );
document.write( "x^2-2x + 1x - 2 = 10<BR>\n" );
document.write( "x^2-x-2 = 10<BR>\n" );
document.write( "x^2-x-2-10 = 0<BR>\n" );
document.write( "x^2-x-12 = 0\r<BR>\n" );
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document.write( "We can factor to solve for x<BR>\n" );
document.write( "x^2-x-12 = 0<BR>\n" );
document.write( "(x-4)(x+3) = 0<BR>\n" );
document.write( "x-4 = 0 or x+3 = 0<BR>\n" );
document.write( "x = 4 or x = -3\r<BR>\n" );
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document.write( "Or we can use the quadratic formula<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ignore the negative x value since it causes either x-2 and x+1 to be negative. <BR>\n" );
document.write( "A negative length or width makes no sense.\r<BR>\n" );
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document.write( "The only practical solution is x = 4.\r<BR>\n" );
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document.write( "If x = 4, then:<BR>\n" );
document.write( "x-2 = 4-2 = 2<BR>\n" );
document.write( "x+1 = 4+1 = 5<BR>\n" );
document.write( "Giving us a 2 ft by 5 ft garden of area 2*5 = 10 sq ft.<BR>\n" );
document.write( "The answer is confirmed.\r<BR>\n" );
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document.write( "Answer: The length of the garden is 5 feet long.<BR>\n" );
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