document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260828>Question 260828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Part of 8,000 was invested at 10% and the rest at 12%. If the annual income from these investments was 860.00 how much was invested at each rate.  I need help with this one.Each rate meaning 10% and 12 % </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192127 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=192127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> total invested is 8,000\r<BR>\n" );
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document.write( "let x be one part.<BR>\n" );
document.write( "let y be the other part.\r<BR>\n" );
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document.write( "you have x + y = 8000 (equation 1)\r<BR>\n" );
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document.write( "total annual income is 860.000\r<BR>\n" );
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document.write( "x part is invested at 10%<BR>\n" );
document.write( "y part is invested at 12%\r<BR>\n" );
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document.write( "you have .10*x + .12*y = 860 (equation 2)\r<BR>\n" );
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document.write( "you need to solve these 2 equations simultaneously.\r<BR>\n" );
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document.write( "solve for y in equation 1 to get y = 8000 - x\r<BR>\n" );
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document.write( "substitute for y in equation 2 to get .10*x + .12*(8000-x) = 860\r<BR>\n" );
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document.write( "solve for x in equation 2.\r<BR>\n" );
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document.write( "equation is:\r<BR>\n" );
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document.write( ".10*x + .12*(8000-x) = 860\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".10*x + .12*8000 - .12*x = 860\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "-.02*x + 960 = 860\r<BR>\n" );
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document.write( "subtract 960 from both sides of this equation to get:\r<BR>\n" );
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document.write( "-.02*x = -100\r<BR>\n" );
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document.write( "divide both sides of this equation by -.02 to get:\r<BR>\n" );
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document.write( "x = 5000\r<BR>\n" );
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document.write( "that means y = 3000 because x + y = 8000.\r<BR>\n" );
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document.write( "you have x = 5000 and y = 3000.\r<BR>\n" );
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document.write( "substitute in equation 2 to get:\r<BR>\n" );
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document.write( ".10*5000 + .12*3000 = 860\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "500 + 360 = 860 which is true confirming the values for x and y are good.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "$5000 was invested at 10% and $3000 was invested at 12%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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