document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284842>Question 284842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam Mathius invested part of his $10,000 bonus in a fund that paid an 11% profit and invested the rest in stock that suffered a 4% loss. Find the amount of each investment if his overall net profit is $650. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206626 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=206626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x equals amount he invested in the fund that paid 11% profit.<BR>\n" );
document.write( "y equals the amount he invested in the fund that suffered a 4% loss.\r<BR>\n" );
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document.write( "His overall net profit was $650.\r<BR>\n" );
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document.write( "You have 2 equations to work with.\r<BR>\n" );
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document.write( "They are:\r<BR>\n" );
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document.write( "x + y = 10,000.\r<BR>\n" );
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document.write( ".11x - .04y = 650\r<BR>\n" );
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document.write( "You need to solve these 2 equations to get your answer.\r<BR>\n" );
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document.write( "solve for y in the first equation to get:\r<BR>\n" );
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document.write( "y = 10,000 - x.\r<BR>\n" );
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document.write( "Substitute that value for y in the second equation to get:\r<BR>\n" );
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document.write( ".11x - .04*(10,000 - x) = 650\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( ".11x - .04*10,000 + .04x = 650\r<BR>\n" );
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document.write( "Combine like terms and simplify further to get:\r<BR>\n" );
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document.write( ".15x - 400 = 650\r<BR>\n" );
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document.write( "Add 400 to both sides of this equation to get:\r<BR>\n" );
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document.write( ".15x = 650 + 400\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( ".15x = 1050\r<BR>\n" );
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document.write( "Divide both sides of this equation by .15 to get:\r<BR>\n" );
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document.write( "x = 7,000\r<BR>\n" );
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document.write( "Since x + y = 10,000, this means that y = 3,000\r<BR>\n" );
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document.write( "Your original equation is:\r<BR>\n" );
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document.write( ".11x - .04y = 650\r<BR>\n" );
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document.write( "Substitute 7,000 for x and 3,000 for y to get:\r<BR>\n" );
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document.write( ".11*7,000 - .04*3,000 = 650\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "770 - 120 = 650 confirming that the values for x and y are good.\r<BR>\n" );
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document.write( "He gained $770 from the 7,000 investment and he lost $120 from the 3,000 investment for a net profit of $650.00\r<BR>\n" );
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document.write( " </SPAN>\n" );
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