document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009023>Question 1009023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 5%, the intermediate-term bonds pay 6%, and the long-term bonds pay 7% simple interest per year. Mark wishes to realize a total annual income of 5.95%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond? \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 #624598 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=624598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = short range<BR>\n" );
document.write( "y = intermediate range<BR>\n" );
document.write( "z = long range.\r<BR>\n" );
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document.write( "x + y + z = 100,000\r<BR>\n" );
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document.write( ".05x + .06y + .07z = .0595 * 100,000 = 5950\r<BR>\n" );
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document.write( "x = y\r<BR>\n" );
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document.write( "replace y with x to get:\r<BR>\n" );
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document.write( "2x + z = 100,000<BR>\n" );
document.write( ".11x + .07z = 5950\r<BR>\n" );
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document.write( "note that .11x is equivalent to .05*x + .06*x.\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 100 and multiply both sides of the first equation by 7 to get:\r<BR>\n" );
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document.write( "14x + 7z = 700,000<BR>\n" );
document.write( "11x + 7z = 595,000\r<BR>\n" );
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document.write( "subtract second equation from the first to get:\r<BR>\n" );
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document.write( "3x = 105,000\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 35,000\r<BR>\n" );
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document.write( "in the first original equation of 2x + z = 100,000, replace x with 35,000 to get 2 * 35,000 + z = 100,000.\r<BR>\n" );
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document.write( "this becomes 70,000 + z = 100,000.\r<BR>\n" );
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document.write( "solve for z to get z = 30,000\r<BR>\n" );
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document.write( "in the second original equation of .11x + .07z = 5950, replace x with 35,000 and replace z with 30,000 to get .11 * 35,000 + .07 * 30,000 = 5950.\r<BR>\n" );
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document.write( "simplify to get 5950 = 5950.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( ".11 * x is equivalent to .05 * x + .06 * x\r<BR>\n" );
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document.write( "since y = x, this is equivalent to .05 * x + .06 * y \r<BR>\n" );
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document.write( "both x and y are equal to 35,000, so this is equivalent to .05 * 35,000 + .06 * 35,000.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( ".05 * 35,000 dollars in short term bonds + .06 * 35,000 in intermediate term bonds + .07 * 30,000 dollars in long term bonds.\r<BR>\n" );
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document.write( "the total money invested is 100,000.\r<BR>\n" );
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document.write( "the total interest earned is 5,950\r<BR>\n" );
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document.write( "5,950 / 100,000 = .0595\r<BR>\n" );
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document.write( ".0595 * 100 = 5.95%.\r<BR>\n" );
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