document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887182>Question 887182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a person invested $8000 for 1 year, part at 8%, part at 11%, and the remainder at 12%.  The total annual income for these investments was $876.  The amount of money invested at 12% was $200 more than the amounts invested at 8% and 11% combined.  Find the amount invested at each rate. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536470 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=536470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = amount invested at 8%<BR>\n" );
document.write( "let y = amount invested at 11%<BR>\n" );
document.write( "let z = amount invested at 12%\r<BR>\n" );
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document.write( "you get 2 equations:\r<BR>\n" );
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document.write( "x + y + z = 8000 and .08x + .11y + .12z = 876\r<BR>\n" );
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document.write( "the mount invested at 12% was $200 more than the  amount invested at 8% and 12%.\r<BR>\n" );
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document.write( "this means that z = 200 + x + y\r<BR>\n" );
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document.write( "replace z with 200 + x + y in both your equations to get:\r<BR>\n" );
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document.write( "x + y + (200 + x + y) = 8000  and .08x + .11y + .12 * (200 + x + y) = 876\r<BR>\n" );
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document.write( "simplify both equations to get:\r<BR>\n" );
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document.write( "2x + 2y + 200 = 7800 and .08x + .11y + .12*200 + .12x + .12y = 876\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "2x + 2y + 200 = 7800 and .2x + .23y + 24 = 876\r<BR>\n" );
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document.write( "subtract 200 from both sides of the first equation and subtract 24 from both sides of the second equation to get:\r<BR>\n" );
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document.write( "2x + 2y = 7800 and .2x + .23y = 852\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 10 to get:\r<BR>\n" );
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document.write( "2x + 2y = 7800 and 2x + 2.3y = 8520\r<BR>\n" );
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document.write( "subtract the first equation from the second equation to get:\r<BR>\n" );
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document.write( ".3y = 720\r<BR>\n" );
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document.write( "divide both sides of this equation by .3 to get:\r<BR>\n" );
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document.write( "y = 2400\r<BR>\n" );
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document.write( "replace y with 2400 in the equation of 2x + 2y = 7800 to get:\r<BR>\n" );
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document.write( "2x + 2(2400) = 7800<BR>\n" );
document.write( "simplify this to get 2x + 4800 = 7800<BR>\n" );
document.write( "subtract 4800 from both sides of this equation to get 2x = 3000<BR>\n" );
document.write( "divide both sides of this equation by 2 to get x = 1500\r<BR>\n" );
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document.write( "you have x = 1500 and y = 2400\r<BR>\n" );
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document.write( "go back to your original equation of x + y + z = 8000 and replace x with 1500 and replace y with 2400 and solve for z to get z = 4100.\r<BR>\n" );
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document.write( "now you have:<BR>\n" );
document.write( "x = 1500<BR>\n" );
document.write( "y = 2400<BR>\n" );
document.write( "z = 4100\r<BR>\n" );
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document.write( "those should be your solutions.<BR>\n" );
document.write( "all that is left is to confirm that they are good solutions.\r<BR>\n" );
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document.write( "x + y + z = 8000 becomes 1500 + 2400 + 4100 = 8000 which becomes 8000 = 8000 so that part is good.\r<BR>\n" );
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document.write( ".08x + .11y + .12z = 876 becomes .08*1500 + .11*2400 + .12*4100 = 876 which becomes 120 + 264 + 492 = 876 which becomes 876 = 876 so that part is good.\r<BR>\n" );
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document.write( "looks like all parts are good so the solution is confirmed as good.\r<BR>\n" );
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document.write( "the amount invested at 8% is 1500<BR>\n" );
document.write( "the amount invested at 11% is 2400<BR>\n" );
document.write( "the amount invested at 12% is 4100\r<BR>\n" );
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document.write( " </SPAN>\n" );
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