document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250919>Question 250919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve using the 5 step problem-solving process. You are pulling a stone border of uniform width around a rectangular garden that measures 6 yards by 15 yards. You only have enough stone to cover 100 square yards. How wide should the border be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182699 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=182699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the measurement of your yard is:\r<BR>\n" );
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document.write( "length 15 yards.<BR>\n" );
document.write( "width = 6 years.\r<BR>\n" );
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document.write( "the area of your yard is 15 * 6 = 90 square yards.\r<BR>\n" );
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document.write( "you want to put a stone border around this yard.\r<BR>\n" );
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document.write( "you have 100 square yards of stone available to you.\r<BR>\n" );
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document.write( "once you ring your yard with the stone border, the total area will be:\r<BR>\n" );
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document.write( "90 square yards + 100 square yards = 190 square yards.\r<BR>\n" );
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document.write( "the border will be the same width all around, so we let the width of the border be equal to x.\r<BR>\n" );
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document.write( "this means that the length of the garden will be increased by 2*x, and the width of the garden will be increased by 2*x (x added to each end equals a total of 2*x).\r<BR>\n" );
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document.write( "our equation for the area of the garden plus the border becomes:\r<BR>\n" );
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document.write( "(2x + 6) * (2x + 15) = 190\r<BR>\n" );
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document.write( "we multiply these factors together to get:\r<BR>\n" );
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document.write( "4x^2 + 30x + 12x + 90 = 190\r<BR>\n" );
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document.write( "we subtract 190 from both sides of this equation and we simplify by combining like terms to get:\r<BR>\n" );
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document.write( "4x^2 + 42x - 100 = 0\r<BR>\n" );
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document.write( "we use the quadratic formula to solve this equation to get:\r<BR>\n" );
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document.write( "x = 2 or x = -12.5\r<BR>\n" );
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document.write( "x has to be positive, so we take x = 2 and substitute in the original equation to confirm that the equation is true meaning that the value of x is good.\r<BR>\n" );
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document.write( "original equation is:\r<BR>\n" );
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document.write( "(2x + 6) * (2x + 15) = 190\r<BR>\n" );
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document.write( "replace x with 2 to get:\r<BR>\n" );
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document.write( "(2*2 + 6) * (2*2 + 15) = 190\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "10 * 19 = 190\r<BR>\n" );
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document.write( "since this equation is true, the value of x = 2 is good.\r<BR>\n" );
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document.write( "the answer to the problem is:\r<BR>\n" );
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document.write( "the width of our border will be 2 yards.\r<BR>\n" );
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document.write( "USE OF QUADRATIC FORMULA\r<BR>\n" );
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document.write( "the quadratic formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-b%29+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-b%29+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the standard form of a quadratic equation is:\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "your formula was:\r<BR>\n" );
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document.write( "4x^2 + 42x - 100 = 0\r<BR>\n" );
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document.write( "this meant that:\r<BR>\n" );
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document.write( "a = 4<BR>\n" );
document.write( "b = 42<BR>\n" );
document.write( "c = -100\r<BR>\n" );
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document.write( "using these values, the quadratic formula became:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-42%29+%2B-+sqrt%2842%5E2-%284%2A4%2A%28-100%29%29%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-42%29+%2B-+sqrt%2842%5E2-%284%2A4%2A%28-100%29%29%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifying made the equation look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-42%29+%2B-+sqrt%281764+%2B+1600%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-42%29+%2B-+sqrt%281764+%2B+1600%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifying further made the equation look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-42%29+%2B-+sqrt%283364%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-42%29+%2B-+sqrt%283364%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifying further made the equation look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-42%29+%2B-+58%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28%28-42%29+%2B-+58%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the rest was just finishing up work by performing the indicated operations.\r<BR>\n" );
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document.write( "FIVE STEP PROCESS\r<BR>\n" );
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document.write( "We followed the 5 step process even though you may not have realized it.\r<BR>\n" );
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document.write( "The 5 step process is as follows:\r<BR>\n" );
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document.write( "1. REad the problem<BR>\n" );
document.write( "2. Choose a variable to represent one quantity. Use that variable to represent every quantity in the problem.<BR>\n" );
document.write( "3. Write an equation relating the quantities in the problem.<BR>\n" );
document.write( "4. Solve your equation and answer the question asked.<BR>\n" );
document.write( "5. Check your answer.\r<BR>\n" );
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document.write( "We read the problem. (step 1)<BR>\n" );
document.write( "We chose the variable x to represent the width of the border (step 2)<BR>\n" );
document.write( "We wrote an equation relating the quantities in the problem.   That was the equation of (2x+6) * (2x+15) = 190 (step 3)<BR>\n" );
document.write( "WE solved the equation and answered the question asked (step 4).<BR>\n" );
document.write( "We checked our answer to confirm that it was good (step 5).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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