document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=415225>Question 415225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to write an algebraic equation to find the volume in gallons for a swimming pool with the following variables:\r<BR>\n" );
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document.write( "Deep End = 8ft<BR>\n" );
document.write( "Shallow End = 3ft\r<BR>\n" );
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document.write( "Length = 20l<BR>\n" );
document.write( "Width = 14w\r<BR>\n" );
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document.write( "How do I write the equation using the syntax:<BR>\n" );
document.write( "Deep end + Shallow end / 2 = Avg. Depth<BR>\n" );
document.write( "Avg. Depth * 20l * 14w * 7.48 = Volume in gallons\r<BR>\n" );
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document.write( "I know there is a way to write the equation with all of these variables into one equation, but I haven't been able to figure it out so far. I can do it in two equations but I need it in one. I have a hard time writing algebra equations so if someone could help me I would greatly appreciate it.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #291171 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=291171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The pool is 3 feet deep at the shallow end and 8 feet deep at the deep end.\r<BR>\n" );
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document.write( "If you assume that the pool is all shallow, then the volume would be 20 * 14 * 3 = 840 cubic feet.\r<BR>\n" );
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document.write( "That's just for the shallow part.\r<BR>\n" );
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document.write( "Take that shallow part away and you are left with a pool that is 5 feet deep.\r<BR>\n" );
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document.write( "This part of the pool gradually increases in depth from 0 feet at the shallow to 5 feet at the deep end.\r<BR>\n" );
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document.write( "The gradual increase in depth is the diagonal of a rectangle.\r<BR>\n" );
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document.write( "This divides the rectangle into 2 triangles that are equal in area to each other.\r<BR>\n" );
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document.write( "The area of the pool that is 5 feet deep is 20 * 14 * 5 = 1400 square feet.\r<BR>\n" );
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document.write( "half of that is equal to 700 square feet.\r<BR>\n" );
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document.write( "The total volume of the water in the pool is 840 + 700 = 1540 cubic feet.\r<BR>\n" );
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document.write( "From google, you get 1 cubic foot = 7.48051948 US gallons\r<BR>\n" );
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document.write( "Since you have 1540 cubic feet, that equates to 11520 gallons of water.\r<BR>\n" );
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document.write( "The average depth of your pool would be 3 feet for the shallow part of the pool plus half of 5 feet for the deeper end of the pool.\r<BR>\n" );
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document.write( "That would be equal to 3 + 5/2 = 3 + 2.5 = 5.5 feet.\r<BR>\n" );
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document.write( "5.5 * 20 * 14 * 7.48051948 = 11520 gallons of water.\r<BR>\n" );
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document.write( "I believe that's how you would do it.\r<BR>\n" );
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document.write( "The first 3 feet have to be added to the average of the depth from 3 feet to 8 feet.\r<BR>\n" );
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document.write( "The average of the first 3 feet is equal to 3 feet because it does that all the way across.\r<BR>\n" );
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document.write( "The depth from 3 feet to 8 is 5 and half of that is 2.5.\r<BR>\n" );
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document.write( "the average depth of the pool is therefore 3 + 2.5 = 5.5 feet.\r<BR>\n" );
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document.write( "Tricky little problem but I believe that's how you would do it in this case.\r<BR>\n" );
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document.write( "Knowing a little geometry helps.\r<BR>\n" );
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document.write( "The average depth being half of the low end and the high end applies to only the bottom 5 feet of the pool.\r<BR>\n" );
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