document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124263>Question 1124263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Things did not go quite as planned. You invested $20,000, part of it in a stock that paid 12% annual interest. However, the rest of the money suffered a 5% loss. If the total annual income from both investments was $2026, how much was invested at each rate?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740627 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=740627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> total amount of money that was invested was 20,000.\r<BR>\n" );
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document.write( "one part of it earned 12%.\r<BR>\n" );
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document.write( "the other part lost 5%.\r<BR>\n" );
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document.write( "x = the part that earned 12%.<BR>\n" );
document.write( "y = the part that lost 5%.\r<BR>\n" );
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document.write( "the total income from both investments was 2026.\r<BR>\n" );
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document.write( "your equation is:\r<BR>\n" );
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document.write( ".12 * x - .05 * y = 2026\r<BR>\n" );
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document.write( "also, x + y = 20,000\r<BR>\n" );
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document.write( "from the second equation, solve for y to get y = 20,000 - x\r<BR>\n" );
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document.write( "in the first equation replace y with 20,000 - x to get:\r<BR>\n" );
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document.write( ".12 * x - .05 * (20,000 - x) = 2026\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".12 * x - .05 * 20,000 + .05 * x = 2026\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( ".17 * x - 1000 = 2026\r<BR>\n" );
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document.write( "add 1000 to both sides of this equation to get:\r<BR>\n" );
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document.write( ".17 * x = 3026\r<BR>\n" );
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document.write( "solve for x to get x = 3026 / .17 = 17,800.\r<BR>\n" );
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document.write( "since x + y = 20,000, and x = 17,800, then y must be equal to 2,200.\r<BR>\n" );
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document.write( "he earned 12% on 17,800 and lost 5% on 2,200.\r<BR>\n" );
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document.write( "his net return was 2136 - 110 = 2026\r<BR>\n" );
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document.write( "that agrees with the problem statement, so the solution looks good.\r<BR>\n" );
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document.write( "the solution is he invested 17,800 that earned 12% and 2,200 that lost 5%.\r<BR>\n" );
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