document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072152>Question 1072152</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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 #687052 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A $70,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%.<BR>\n" );
document.write( " The bond and CD investment together must equal the mortgage investment.<BR>\n" );
document.write( " To earn a $6430 annual income from the investments, how much should the bank invest in bonds?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let b = amt invested in bonds <BR>\n" );
document.write( "let c = amt invested in CD's<BR>\n" );
document.write( "let m = amt invested in Mortgages<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b + c + m = 70000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"The bond and CD investment together must equal the mortgage investment.\"<BR>\n" );
document.write( "m = (b+c)<BR>\n" );
document.write( "therefore we can replace m with (b+c)<BR>\n" );
document.write( "b + c + (b+c) = 70000<BR>\n" );
document.write( "2b + 2c = 70000<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "b + c = 35000<BR>\n" );
document.write( "c = 35000 - b; we can use this form for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"To earn a $6430 annual income from the investments, how much should the bank invest in bonds?\"<BR>\n" );
document.write( ".09b + .07c + .10m = 6430<BR>\n" );
document.write( "Replace m with (b+c)<BR>\n" );
document.write( ".09b + .07c + .10(b+c) = 6430<BR>\n" );
document.write( ".09b + .07c + .10b + .10c = 6430<BR>\n" );
document.write( ".19b + .17c = 6430<BR>\n" );
document.write( "Replace c with (35000-b)<BR>\n" );
document.write( ".19b + .17(35000-b) = 6430<BR>\n" );
document.write( ".19b + 5950 - .17b = 6430<BR>\n" );
document.write( ".19b - .17b = 6430 - 5950<BR>\n" );
document.write( ".02b = 480<BR>\n" );
document.write( "b = 480/.02<BR>\n" );
document.write( "b = $24,000 in vested in bonds<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Confirm this by finding c and m, then finding the total interest<BR>\n" );
document.write( "c: 35000-24000 = 11000<BR>\n" );
document.write( "m: 24000+11000 = 35000<BR>\n" );
document.write( ".09(24000) = 2160<BR>\n" );
document.write( ".07(11000) =  770<BR>\n" );
document.write( ".10(35000) = 3500<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "total int: 6430<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );