document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206271>Question 1206271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ​Betsy, a recent​ retiree, requires ​$6,000 per year in extra income.  She has ​$50,000 to invest and can invest in​ B-rated bonds paying 17​% per year or in a certificate of deposit​ (CD) paying 7​% per year.  How much money should be invested in each to realize exactly ​$6,000  in interest per​ year? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843580 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=843580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she needs 6000 per year.<BR>\n" );
document.write( "she has:<BR>\n" );
document.write( "50,000 total to invest.<BR>\n" );
document.write( "b-rated bonds pay 17% per year<BR>\n" );
document.write( "certificates of deposit pay 7% per year.<BR>\n" );
document.write( "let x = value in b-rated bonds.<BR>\n" );
document.write( "let y = value in certificates of deposit.<BR>\n" );
document.write( "you have two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "x + y = 50,000<BR>\n" );
document.write( ".17x + .07y = 6,000<BR>\n" );
document.write( "the overall interest rate will be 12% because .12 * 50,000 = 6000.<BR>\n" );
document.write( "this was just a check to make sure that the highest interest rate investment would be enough to cover her interest requirements.<BR>\n" );
document.write( "it does.<BR>\n" );
document.write( "multiply both sides of the first equation by .17 and leave the second equation as is to get:<BR>\n" );
document.write( ".17x + .17y = 8500<BR>\n" );
document.write( ".17x + .07y = 6000<BR>\n" );
document.write( "subtract the second equation from the first to get:<BR>\n" );
document.write( ".10y = 2500<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 25000\r<BR>\n" );
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document.write( "looks like she should invest 25000 in b-rated bonds and 25000 in certificates of deposit.<BR>\n" );
document.write( "original equations becomes:<BR>\n" );
document.write( "x + y = 25000 + 25000 = 50,000<BR>\n" );
document.write( ".17x + .07y = 4250 + 1750 = 6000.\r<BR>\n" );
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document.write( "your solution is she should invest 25000 in b-rated bonds paying 17% and 25000 in certificates of deposit paying 7% to get a total annual interest of 6000 from both.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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