document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164971>Question 164971</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078651131/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem.\r<BR>\n" );
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document.write( "An alloy of metals is 25% copper.  ANother alloy is 50% copper.  how much of each alloy should be used to make 1000 grams of an alloy that is 45% copper? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121612 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An alloy of metals is 25% copper.  Another alloy is 50% copper.  how much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?\r<BR>\n" );
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document.write( "We have a system of equation in two variables.\r<BR>\n" );
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document.write( "Let x = alloy of metal\r<BR>\n" );
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document.write( "Let y = Another alloy\r<BR>\n" );
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document.write( "THEN:\r<BR>\n" );
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document.write( "x + y = 1000...Equation A\r<BR>\n" );
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document.write( "The question tells us that 25% is copper and that the other alloy is 50% copper.\r<BR>\n" );
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document.write( "From this information we make our second equation.\r<BR>\n" );
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document.write( "0.25x + 0.50x = 0.45 (1000)...Equation B\r<BR>\n" );
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document.write( "Here is your system of equations:\r<BR>\n" );
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document.write( "x + y = 1000...Equation A\r<BR>\n" );
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document.write( "0.25x + 0.50y = 0.45 (1000)...Equation B\r<BR>\n" );
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document.write( "I will solve for y in Equation A. Of course, you can solve for x or y (your choice).\r<BR>\n" );
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document.write( "From this system of equations, it is easier playing with equation A.\r<BR>\n" );
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document.write( "x + y = 1000...Equation A\r<BR>\n" );
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document.write( "Solving for x, I get:\r<BR>\n" );
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document.write( "x = 1000 - y\r<BR>\n" );
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document.write( "I will now plug x = 1000 - y into Equation B to find the value of y.\r<BR>\n" );
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document.write( "0.25x + 0.50y = 0.45 times (1000)\r<BR>\n" );
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document.write( "0.25(1000 - y) + 0.50y = 450\r<BR>\n" );
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document.write( "250 - 0.25y + 0.50y = 450\r<BR>\n" );
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document.write( "250 + 0.25y = 450\r<BR>\n" );
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document.write( "0.25y = 450 - 250\r<BR>\n" );
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document.write( "0.25y = 200\r<BR>\n" );
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document.write( "y = 200/0.25\r<BR>\n" );
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document.write( "y = 800\r<BR>\n" );
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document.write( "We just found the value of y to be 800.\r<BR>\n" );
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document.write( "To find x, we plug y = 800 for y in EITHER Equation A or Equation B.\r<BR>\n" );
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document.write( "I will select the easy Equation A.\r<BR>\n" );
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document.write( "x + y = 1000...Equation A\r<BR>\n" );
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document.write( "x + 800 = 1000\r<BR>\n" );
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document.write( "Solving for x, I get:\r<BR>\n" );
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document.write( "x = 1000 - 800\r<BR>\n" );
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document.write( "x = 200\r<BR>\n" );
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document.write( "Finals answer:  200 alloy of metal should be used and 800 of the other alloy should be used.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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