document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106454>Question 1106454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person has 30,000 to invest. As the person's financial consultant, you recommend that the money be invested in Treasury Bills yielding 2%, Treasury Bonds yielding 4% and Corporate Bonds yielding 6%. The person wants an annual income of $1120 and the amount invested in Corporate Bonds must be half that in Treasury Bills. Find amount for each.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721522 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=721522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person has 30,000 to invest.<BR>\n" );
document.write( "a + b + c = 30000<BR>\n" );
document.write( " As the person's financial consultant, you recommend that the money be invested in:<BR>\n" );
document.write( " Treasury Bills yielding 2%,<BR>\n" );
document.write( "let a = T bills<BR>\n" );
document.write( " Treasury Bonds yielding 4% and<BR>\n" );
document.write( "let b = T bonds <BR>\n" );
document.write( " Corporate Bonds yielding 6%.<BR>\n" );
document.write( "let c = Corp bonds <BR>\n" );
document.write( "The person wants an annual income of $1120<BR>\n" );
document.write( ".02a + .04b + .06c = 1120<BR>\n" );
document.write( ":<BR>\n" );
document.write( " and the amount invested in Corporate Bonds must be half that in Treasury Bills.<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >a<BR>\n" );
document.write( "or<BR>\n" );
document.write( "a = 2b<BR>\n" );
document.write( ":<BR>\n" );
document.write( "replace a with 2b in both equations<BR>\n" );
document.write( "2b + b + c = 3000<BR>\n" );
document.write( "3b + c = 30000<BR>\n" );
document.write( "and<BR>\n" );
document.write( ".02(2b) + .04b + .06c = 1120<BR>\n" );
document.write( ".08b + .06c = 1120<BR>\n" );
document.write( ".08b = -.06c + 1120<BR>\n" );
document.write( "Divide eq by .08<BR>\n" );
document.write( "b = -.75c + 14000<BR>\n" );
document.write( "Substitute this equation in 3b + c = 3000<BR>\n" );
document.write( "3(-.75c+14000) + c = 30000<BR>\n" );
document.write( "distribute the 3<BR>\n" );
document.write( "-2.25c + 42000 + c = 30000<BR>\n" );
document.write( "-1.25c = 30000 - 42000<BR>\n" );
document.write( "-1.25c = -12000<BR>\n" );
document.write( "c = -12000/-1.25<BR>\n" );
document.write( "c = +$9600 in Corp bonds<BR>\n" );
document.write( "Find b<BR>\n" );
document.write( "b = -.75(9600) + 14000<BR>\n" );
document.write( "b = -7200 + 14000<BR>\n" );
document.write( "b = $6800 in T bonds<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "a = 2(6800)<BR>\n" );
document.write( "a = $13600 in T bills<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Find amount for each. $13600, $6800, $9600<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "confirm this<BR>\n" );
document.write( ".02(13600) = 272<BR>\n" );
document.write( ".04(6800) = 272<BR>\n" );
document.write( ".06(9600) = 576<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "total income: 1120  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );