document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203028>Question 1203028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By volume, one alloy is 60, copper, 30, zinc, and 10, nickel. A second alloy has percents of 50,<BR>\n" );
document.write( "30, and 20, respectively. A third alloy is 30, copper and 70, nickel. How much of each alloy is<BR>\n" );
document.write( "needed to make 100 cm3 of a resulting alloy with percents of 40, 15, and 45, respectively? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838258 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=838258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Actually, it is very naïve approach to think that volume of an alloy is the sum of volumes of composites.\r<BR>\n" );
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document.write( "It is well known fact for all metallurgists just more than several hundreds years <BR>\n" );
document.write( "that due to shrinking effect, the volume of an alloy, as a rule, is not equal to the sum <BR>\n" );
document.write( "of volumes of composite metals.\r<BR>\n" );
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document.write( "I know and remember it from learning Science in my middle school years <BR>\n" );
document.write( "(which means that this phenomenon is of the commonly known level of knowledge).\r<BR>\n" );
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document.write( "For further information and to develop your knowledge, look, read and learn from these sources\r<BR>\n" );
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document.write( "https://www.diva-portal.org/smash/get/diva2:218833/FULLTEXT01.pdf\r<BR>\n" );
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document.write( "https://nvlpubs.nist.gov/nistpubs/jres/8/jresv8n1p37_A2b.pdf   \r<BR>\n" );
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document.write( "    (publication of the 1932 year).\r<BR>\n" );
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document.write( "Having enough free time, anyone can find hundred of articles, tens textbooks, monographs <BR>\n" );
document.write( "and handbooks in metallurgy and material science that teach this phenomenon, which is important<BR>\n" );
document.write( "and essential for alloys.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Therefore, a competent Math problems composer will NEVER <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;propose such a problem, as in this post, to school students.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Masses can be added for alloys, but volumes not.\r<BR>\n" );
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document.write( "Adding volumes of alloys to find the volume of the final product is the sign of a general <BR>\n" );
document.write( "incompetence in the subject.\r<BR>\n" );
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document.write( "If in this problem the numbers / (the quantities) be the masses in consistent units,<BR>\n" );
document.write( "it would be a normal / (correct) problem with the solution as in the post by another tutor.\r<BR>\n" );
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document.write( "But with the given interpretation, when the given quantities are the VOLUMES,<BR>\n" );
document.write( "the problem is like a lame horse and does not suit for proper teaching of students.\r<BR>\n" );
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document.write( "The cause WHY the volume of the resulting alloy is not the sum of volumes <BR>\n" );
document.write( "of participating components is that crystal structure of the resulting alloy <BR>\n" );
document.write( "is DIFFERENT from that of the components.\r<BR>\n" );
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document.write( "The phenomenon I am talking about, is close (although is not identical) <BR>\n" );
document.write( "to the fact that the volume of ice is greater than the volume of water.\r<BR>\n" );
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document.write( "It is why icebergs float on the surface of water . . . \r<BR>\n" );
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document.write( " </SPAN>\n" );
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