document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107664>Question 107664</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/536965943/algebrahomeworkh>beggining algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 27.  How much of an alloy that is 20% copper should be mixed with 200ounces of an alloy that is 50% copper in order to get an alloy of 30% copper? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78440 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want to know how much 20% copper alloy, so let that be x.  We also don't know the total amount of 30% alloy, so let that be y.\r<BR>\n" );
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document.write( "Now, let's figure out what we do know.\r<BR>\n" );
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document.write( "The amount of 20% alloy plus the 200 oz. of 50% alloy must equal the amount of 30% alloy, so:\r<BR>\n" );
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document.write( "Eq 1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B200=y ALIGN=MIDDLE  ALT=\"x%2B200=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We also know that the amount of copper in the 20% alloy is 0.2x, the amount of copper in the 50% alloy is 50% of 200 oz, or 100 oz, and the amount of copper in the 30% alloy must be 0.3y.  We also know that the copper in the 20% alloy plus the copper in the 50% alloy must equal the copper in the 30% alloy.  Therefore:\r<BR>\n" );
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document.write( "Eq 2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2x%2B100=0.3y ALIGN=MIDDLE  ALT=\"0.2x%2B100=0.3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now it is a matter of solving two simultaneous linear equations in two variables.  There are a number of methods, but this is the one I like.  First re-arrange the equations to standard form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Or, in this case:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y%2B200=0 ALIGN=MIDDLE  ALT=\"x-y%2B200=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2x-0.3y%2B100=0 ALIGN=MIDDLE  ALT=\"0.2x-0.3y%2B100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then I multiply the 2nd equation by -5:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B1.5y-500=0 ALIGN=MIDDLE  ALT=\"-x%2B1.5y-500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then add the result to the first equation, term by term:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0.5y-300=0 ALIGN=MIDDLE  ALT=\"0x%2B0.5y-300=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5y=300 ALIGN=MIDDLE  ALT=\"0.5y=300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=600 ALIGN=MIDDLE  ALT=\"y=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B200=600 ALIGN=MIDDLE  ALT=\"x%2B200=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=400 ALIGN=MIDDLE  ALT=\"x=400\"   DISABLED_style= \"max-width:90%; height:auto;\" >ounces.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2B200=600 ALIGN=MIDDLE  ALT=\"400%2B200=600\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2%2A400%2B0.5%2A200=0.3%2A600 ALIGN=MIDDLE  ALT=\"0.2%2A400%2B0.5%2A200=0.3%2A600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80+%2B+100+=+180 ALIGN=MIDDLE  ALT=\"80+%2B+100+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Check!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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