document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113878>Question 113878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many grams of pure silver must be mixed with 450grams of an alloy that is 10% copper in order to produce a sterling silver that is 7.5% copper? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82865 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font face = \"lucida console\"><b>\r\n" );
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document.write( "How many grams of pure silver must be mixed with 450 grams of an alloy that\r\n" );
document.write( "is 10% copper in order to produce a sterling silver that is 7.5% copper?\r\n" );
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document.write( "We have three things to consider: 1. the first stuff, 2. the second \r\n" );
document.write( "stuff, and 3. the final stuff that we get after we mix the first stuff\r\n" );
document.write( "with the second stuff.\r\n" );
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document.write( "Each of those \"stuffs\" contains some pure copper, and/or some pure silver,\r\n" );
document.write( "and/or some other stuff.    \r\n" );
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document.write( "So we mix: \r\n" );
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document.write( "1.  x grams of the first stuff that is 100% silver and therefore 0% copper\r\n" );
document.write( "and 0% other metal.\r\n" );
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document.write( "with\r\n" );
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document.write( "2.  450 grams of the second stuff that is 10% copper and therefore 90% other\r\n" );
document.write( "metal and 0% silver\r\n" );
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document.write( "and end up with\r\n" );
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document.write( "3. x+450 grams of the final stuff that is 7.5% copper and therefore 92.5%\r\n" );
document.write( "silver and other metal.\r\n" );
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document.write( "Note: it isn't necessary to deal with anything but the copper, but I\r\n" );
document.write( "think it makes it easier to deal with all the ingredients.\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "                grams of   grams of    grams of    grams of\r\n" );
document.write( "                 stuff      silver      copper     other metal\r\n" );
document.write( "first stuff                                               \r\n" );
document.write( "second stuff                                                \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "final stuff                                                  \r\n" );
document.write( "                                             \r\n" );
document.write( "Fill in the number of grams of the first, second and final stuff.  That is,\r\n" );
document.write( "x grams of the first stuff, 450 grams of the second stuff, and therefore\r\n" );
document.write( "x+450 grams of the final stuff:\r\n" );
document.write( "    \r\n" );
document.write( "                grams of   grams of    grams of    grams of\r\n" );
document.write( "                 stuff      silver      copper     other metal\r\n" );
document.write( "first stuff         x                                                       \r\n" );
document.write( "second stuff      450                                      \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "final stuff     x+450                                       \r\n" );
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document.write( "Next fill in the number of grams of silver only, by multiplying\r\n" );
document.write( "the grams of the first and second stuff by the percentage of silver \r\n" );
document.write( "expressed as a decimal. The first stuff is 100% silver. The second\r\n" );
document.write( "stuff is 0& silver. Then since the second stuff contains no silver,\r\n" );
document.write( "the final stuff contains exactly the same amount of silver as the \r\n" );
document.write( "first stuff.\r\n" );
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document.write( "                grams of   grams of    grams of    grams of\r\n" );
document.write( "                 stuff      silver      copper     other metal\r\n" );
document.write( "first stuff         x        1.00x                             \r\n" );
document.write( "second stuff      450        0.00(450)                     \r\n" );
document.write( "----------------------------------------------------------\r\n" );
document.write( "final stuff     x+450        1.00x                        \r\n" );
document.write( "                   \r\n" );
document.write( "Next fill in the number of grams of copper only, by multiplying\r\n" );
document.write( "the grams of each stuff by their percentage of copper \r\n" );
document.write( "expressed as a decimal. \r\n" );
document.write( "\r\n" );
document.write( "                grams of   grams of    grams of    grams of\r\n" );
document.write( "                 stuff      silver      copper     other metal\r\n" );
document.write( "first stuff         x        1.00x       0.00x         \r\n" );
document.write( "second stuff      450        0.00(450)   0.10(450)      \r\n" );
document.write( "----------------------------------------------------------\r\n" );
document.write( "final stuff     x+450        1.00x    0.075(x+450)      \r\n" );
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document.write( "Next fill in the number of grams of other metal only, by multiplying\r\n" );
document.write( "the grams of the first and final stuff by their percentage of silver \r\n" );
document.write( "expressed as a decimal. Then since the first stuff contains no\r\n" );
document.write( "\"other metal\", the final stuff contains exactly the same amount of other\r\n" );
document.write( "metal as the second stuff.\r\n" );
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document.write( "                grams of   grams of    grams of    grams of\r\n" );
document.write( "                 stuff      silver      copper     other metal\r\n" );
document.write( "first stuff         x        1.00x       0.00x      0.00x\r\n" );
document.write( "second stuff      450        0.00(450)   0.10(450)  0.90(450)\r\n" );
document.write( "---------------------------------------------------------------\r\n" );
document.write( "final stuff     x+450        1.00x    0.075(x+450)  0.90(450)\r\n" );
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document.write( "Now we can make the \"stuff equation\" out of the first column:\r\n" );
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document.write( "x + 450 = x + 450\r\n" );
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document.write( "But that equation doesn't do us any good.\r\n" );
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document.write( "We can make the \"silver equation\" out of the second column:\r\n" );
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document.write( "1.00x + 0.00(450) = 1.00x\r\n" );
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document.write( "But that equation becomes x = x and does us no good either.\r\n" );
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document.write( "We can make the \"copper equation\" out of the third column:\r\n" );
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document.write( ".00x + .10(450) = 0.075(x+450)\r\n" );
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document.write( "Now that equation shows promise!!\r\n" );
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document.write( "We can make the \"other metal equation\" out of the fourth column:\r\n" );
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document.write( ".00x + .90(450) = .90(450)\r\n" );
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document.write( "That equation becomes 405 = 405 and does us no good.  So we only\r\n" );
document.write( "have one equation that does us any good, the copper equation:\r\n" );
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document.write( ".00x + .10(450) = 0.075(x+450) or\r\n" );
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document.write( "       .10(450) = 0.075(x+450)\r\n" );
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document.write( "Solve that for x and we get x = 150 grams of pure silver  \r\n" );
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document.write( "Edwin</PRE></b></font><BR>\n" );
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