document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072150>Question 1072150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve using system of linear equations.\r<BR>\n" );
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document.write( "A $70,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $6430 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 #687040 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=687040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let:\r<BR>\n" );
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document.write( "a = investment in bonds.<BR>\n" );
document.write( "b = investment in CDs.<BR>\n" );
document.write( "c = investment in mortgages.\r<BR>\n" );
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document.write( "total investment is equal to 70,000.\r<BR>\n" );
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document.write( "a + b + c = 70,000\r<BR>\n" );
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document.write( "total interest is equal to 6,430.\r<BR>\n" );
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document.write( ".09 * a + .07 * b + .10 * c = 6,430.\r<BR>\n" );
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document.write( "investment in bonds and CDs must be equal to investment in mortgages.\r<BR>\n" );
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document.write( "a + b = c\r<BR>\n" );
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document.write( "you have 2 equations that needs to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "a + b + c = 70,000\r<BR>\n" );
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document.write( ".09 * a + .07 * b + .10 * c = 6,430.\r<BR>\n" );
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document.write( "you are given that a + b = c\r<BR>\n" );
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document.write( "you can use this information to reduce the number of unknown variables that have to be solved.\r<BR>\n" );
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document.write( "replace c with a + b in both equations and you get:\r<BR>\n" );
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document.write( "a + b + c = 70,000 becomes a + b + a + b = 70,000 which becomes 2 * a + 2 * b = 70,000.\r<BR>\n" );
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document.write( ".09 * a + .07 * b + .10 * c = 6,430 becomes .09 * a + .07 * b + .10 * (a + b) = 6,430 which becomes .09 * a + .07 * b + .10 * a + .10 * b = 6,430 which becomes .19 * a + .19 * b = 6,430.\r<BR>\n" );
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document.write( "your 2 equations now become:\r<BR>\n" );
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document.write( "2 * a + 2 * b = 70,000\r<BR>\n" );
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document.write( ".19 * a + .17 * b = 6,430\r<BR>\n" );
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document.write( "in the first equation, solve for a to get:\r<BR>\n" );
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document.write( "a = 35,000 -b\r<BR>\n" );
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document.write( "in the second equation, replace a with 35,000 - b to get:\r<BR>\n" );
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document.write( ".19 * (35,000 - b) + .17 * b = 6,430.\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "6,650 - .19 * b + .17 * b = 6,430.\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "6,650 - .02 * b = 6,430\r<BR>\n" );
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document.write( "solve for b to get b = 220 / .02 = 11,000\r<BR>\n" );
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document.write( "since a = 35,000 - b, you get a = 24,000\r<BR>\n" );
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document.write( "since c = a + b, you get c = 35,000\r<BR>\n" );
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document.write( "you can confirm by replacing a with 24,000 and b with 11,000 and c with 35,000 in the original equations to see if they are true.\r<BR>\n" );
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document.write( "the original equations are:\r<BR>\n" );
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document.write( "a + b + c = 70,000\r<BR>\n" );
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document.write( ".09 * a + .07 * b + .10 * c = 6,430.\r<BR>\n" );
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document.write( "replace a with 24,000 and b with 11,000 and c with 35,000 to get:\r<BR>\n" );
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document.write( "24,000 + 11,000 + 35,000 = 70,000 which becomes 70,000 = 70,000 which is true.-\r<BR>\n" );
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document.write( ".09 * 24,000 + .07 * 11,000 + .10 * 35,000 = 6,430 which becomes 6,430 = 6,430 which is true.\r<BR>\n" );
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document.write( "both original equations are true, so the solution is good.\r<BR>\n" );
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document.write( "you were asked how much should be invested in bonds.\r<BR>\n" );
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document.write( "the answer is 24,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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