document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082675>Question 1082675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A $128,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $11,980 annual income from the investments, how much should the bank invest in bonds? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696744 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=696744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> total investment is 128,000.\r<BR>\n" );
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document.write( "it is invested in bonds paying 9%, CEDs paying 8% and mortgages paying 10%.\r<BR>\n" );
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document.write( "the sum of the bond and CD investments must equal mortgage investment.\r<BR>\n" );
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document.write( "let b equal the amount invested in bonds.<BR>\n" );
document.write( "let c equal the amount invested in CDs.<BR>\n" );
document.write( "let d equal the amount invested in mortgages.\r<BR>\n" );
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document.write( "total investment is 128,000\r<BR>\n" );
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document.write( "b + c + d = 128,000\r<BR>\n" );
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document.write( "total income per year is equal to 11,980.\r<BR>\n" );
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document.write( ".09b + .08c + .10d = 11,980\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "b + c + d = 128,000<BR>\n" );
document.write( ".09b + .08c + .10d = 11,980\r<BR>\n" );
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document.write( "you are given that the sum of the bond and CD investment must be equal to the mortgage investment.\r<BR>\n" );
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document.write( "b + c = d\r<BR>\n" );
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document.write( "in the 2 equations that need to be solved simultaneously, replace d with b + d to get:\r<BR>\n" );
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document.write( "b + c + b + c = 128,000<BR>\n" );
document.write( ".09b + .08c + .10(b + c) = 11,980\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "b + c + b + c = 128,000<BR>\n" );
document.write( ".09b + .08c + .10b + .10c = 11,980\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "2b + 2c = 128,000<BR>\n" );
document.write( ".19b + .18c = 11,980\r<BR>\n" );
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document.write( "you have now reduced the number of variables to 2 in 2 equations which can be solved.\r<BR>\n" );
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document.write( "this can be solved in various ways.<BR>\n" );
document.write( "we'll use elimination.\r<BR>\n" );
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document.write( "multiply both sides of second equation by (2/.19) and leave the first equation as is to get:\r<BR>\n" );
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document.write( "2b + 2c = 128,000<BR>\n" );
document.write( "2b + 1.894736842c = 126,105.2632\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( ".1052631579c = 1894.736842\r<BR>\n" );
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document.write( "solve for c to get c = 1894.736841 / .1052631579 = 18,000\r<BR>\n" );
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document.write( "2c is therefore equal to 36,000\r<BR>\n" );
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document.write( "in the equation of 2b + 2c = 128,000, replace 2c with 36,000 to get:\r<BR>\n" );
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document.write( "2b + 36,000 = 128,000\r<BR>\n" );
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document.write( "solve for b to get:\r<BR>\n" );
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document.write( "b = (128,000 - 36,000) / 2.\r<BR>\n" );
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document.write( "this makes b = 46,000.\r<BR>\n" );
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document.write( "in the equation of b + c + d = 128,000, solve for d to get:\r<BR>\n" );
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document.write( "d = 128,000 - 18,000 - 46,000.\r<BR>\n" );
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document.write( "this makes d = 64,000\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "b = 46,000<BR>\n" );
document.write( "c = 18,000<BR>\n" );
document.write( "d = 64,000\r<BR>\n" );
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document.write( "b + c + d is now equal to 46,000 + 18,000 + 64,000 = 128,000\r<BR>\n" );
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document.write( ".09b + .08c + .10d is now equal to .09*46,000 + .08*18,000 + .10*64,000.\r<BR>\n" );
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document.write( "this becomes equal to 4140 + 1440 + 6400 which is equal to 11,980.\r<BR>\n" );
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document.write( "the amount invested in bonds and cd's is 18,000 + 46,000 = 64,000 which is equal to the amount invested in mortgages.\r<BR>\n" );
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document.write( "all the requirements of the problem are satisfied, so the solution looks good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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