document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447437>Question 447437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure exactly which category this goes under. I have a very long math problem I'm struggling to solve. I've googled and seen parts of it or similar problems, but I haven't seen the full thing, so I'm not entirely sure how to go about solving this. Any help will be appreciated, so I thank you in advance. I will also post the parts I think I already worked out so that you can see what I've done so far.\r<BR>\n" );
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document.write( "A gardener has a rose garden that measures 30 feet by 20 feet. He wants to put a uniform border of pine bark around the outside of the garden. Let x be the width of the border in feet. Write an expression for the total area of the border in terms of the width x.<BR>\n" );
document.write( "I came up with 4x^2 + 100x as my answer. Correct?\r<BR>\n" );
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document.write( "Find out how wide the border should be if he has enough pine bark to cover 336 square feet. <BR>\n" );
document.write( "I came up with 3 feet as my answer. Correct?\r<BR>\n" );
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document.write( "If the border needs to be covered to a depth of 3 inches and pine bark costs $29 per cubic yard, what will the material cost to lay the pine bark border? Assume that you must purchase a whole number of cubic yards and not a fraction of a cubic yard.<BR>\n" );
document.write( "Here's where I'm struggling with *how* to answer this one. I came up with $6786, but I'm thinking that's way off. Any advice or suggestions?\r<BR>\n" );
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document.write( "Also, now assume you can actually buy as much or as little bark as you need to cover the border area, that is, the vendor will sell even a small fraction of a cubic yard if you want. Write an expression for the cost in dollars as a function of the width x, of the border in feet. Assume again that the border is to be covered to a depth of 3 inches and that pine bark costs $29 per cubic yard.<BR>\n" );
document.write( "Please help! :) Thanks!\r<BR>\n" );
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document.write( "(There are actually two more questions to this problem, but I'm hoping the above, when I'm able to figure it out, will help me in solving them.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308023 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=308023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A gardener has a rose garden that measures 30 feet by 20 feet. <BR>\n" );
document.write( "He wants to put a uniform border of pine bark around the outside of the garden. Let x be the width of the border in feet. <BR>\n" );
document.write( "Write an expression for the total area of the border in terms of the width x.<BR>\n" );
document.write( "I came up with 4x^2 + 100x as my answer. Correct?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Draw the picture:<BR>\n" );
document.write( "You have a rectangle inside a rectangle.<BR>\n" );
document.write( "The area of the larger rectangle is (30+2x)(20+2x)<BR>\n" );
document.write( "The area of the inside rectangle is 30*20<BR>\n" );
document.write( "So the area of the border is (30+2x)(20+2x)-30*20 = 4x^2+100x sq. ft.<BR>\n" );
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document.write( "Find out how wide the border should be if he has enough pine bark to cover 336 square feet. <BR>\n" );
document.write( "I came up with 3 feet as my answer. Correct?<BR>\n" );
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document.write( "Solve 4x^2+100x = 336<BR>\n" );
document.write( "x^2+25x-84 = 0<BR>\n" );
document.write( "(x-3)(x+28) = 0<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "x = 3 ft.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "If the border needs to be covered to a depth of 3 inches and pine bark costs $29 per cubic yard, what will the material cost to lay the pine bark border? Assume that you must purchase a whole number of cubic yards and not a fraction of a cubic yard.<BR>\n" );
document.write( "Volume = (area)(depth) = 336 sq.ft * (0.25 ft) = 84 cu. ft <BR>\n" );
document.write( "84 cu ft = 84/27 = 3.111 cu yrd<BR>\n" );
document.write( "Price = 3.1111*$29 = $90.22<BR>\n" );
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document.write( "Also, now assume you can actually buy as much or as little bark as you need to cover the border area, that is, the vendor will sell even a small fraction of a cubic yard if you want. Write an expression for the cost in dollars as a function of the width x, of the border in feet. Assume again that the border is to be covered to a depth of 3 inches and that pine bark costs $29 per cubic yard.<BR>\n" );
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document.write( "Volume = (area)(depth)<BR>\n" );
document.write( "Volume = [(4x^2+100x)(1/4)]/27  = (27/4)(4x^2+100x) cu. yds<BR>\n" );
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document.write( "Cost = (29*27/4)(4x^2-100x) = 195.75*4(x^2-25x) = 783(x^2-25x) dollars<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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