document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044390>Question 1044390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An amount of cement, sand, and gravel, mixed in the ratio 1-2-4 (1 part cement, 2 parts sand, 4 parts gravel) are needed to make 1 cu. yd. of solid concrete, allowing 33 1/3% voids (air spaces) in the sand and 45% voids in the gravel.  Determine amount(cu. yds.) of each. \r<BR>\n" );
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document.write( "Solution provided with problem: \r<BR>\n" );
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document.write( "Let x = cu. yd. of cement. \r<BR>\n" );
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document.write( "Let y = cu. yd. of sand. \r<BR>\n" );
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document.write( "Let z = cu. yd. of gravel. \r<BR>\n" );
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document.write( "The voids are filled in finished concrete and the z cu. yd. count only as .55z cu. yd. of solid concrete, and the y cu. yd. of sand count only at 2/3y cu. yd. of gravel.  No voids in the cement. \r<BR>\n" );
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document.write( "Equations: \r<BR>\n" );
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document.write( "(1) x + 2/3y + .55z = 1 (cu. yd. of concrete) \r<BR>\n" );
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document.write( "(2) y = 2x and z = 4x, from ratios in mixture. \r<BR>\n" );
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document.write( "Substituting values of y and z from (2) in (1), \r<BR>\n" );
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document.write( "x + 4x/3 + 2.2x = 1 \r<BR>\n" );
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document.write( "Please explain solution. \r<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 #659713 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "I think that this scheme is infinitely far from reality. \r<BR>\n" );
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document.write( "And has nothing common with the reality.\r<BR>\n" );
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document.write( "So there is no sense to consider it and to try to solve.\r<BR>\n" );
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document.write( "Let us consider the equation (1) and, in particular, the term 0.55z.\r\n" );
document.write( "It is z - 0.45z.\r\n" );
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document.write( "Do you assume that the gravel consolidates/compresses \"inside itself\" (implodes) to zeroes its own porosity ?\r\n" );
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document.write( "Same question about the addend <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%2Ay ALIGN=MIDDLE  ALT=\"%282%2F3%29%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" > for sand.\r\n" );
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document.write( "Do you know that a significant amount of water is needed and is used to produce concrete ?\r\n" );
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document.write( "Where is the water in your balance ?\r\n" );
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document.write( "The mechanism and the scheme of forming concrete is much more complicated.\r\n" );
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document.write( "The scheme in this post/solution is totally inadequate.\r\n" );
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