document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=607390>Question 607390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> $10,000 is to be invested in three different ways. One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year. The remainder is put in the bank at 5% annual interest. In the first year, the investments bring a return of $830. How much was invested in each way?\r<BR>\n" );
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document.write( "This is a matrices problem but I am confused with how to begin with the equations. <BR>\n" );
document.write( "Is one equation x + y + z = 10,000? The second equation.. Is is something like this? 0.08x + 2(0.09)y = \r<BR>\n" );
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document.write( "I will be able to solve the problem after understanding how to put the wording into equations.. I understand how to solve matrices, so I am not asking for help with that. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #382787 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=382787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> $10,000 is to be invested in three different ways.<BR>\n" );
document.write( " One part of the money is used to purchase mutual fund that offer a return of 8% per year. <BR>\n" );
document.write( "The second part, which amounts to twice the first, is used to buy government bonds at 9% per year.<BR>\n" );
document.write( " The remainder is put in the bank at 5% annual interest.<BR>\n" );
document.write( " In the first year, the investments bring a return of $830.<BR>\n" );
document.write( " How much was invested in each way?<BR>\n" );
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document.write( "Let x = amt invested at 8%<BR>\n" );
document.write( "Let y = amt invested at 9%<BR>\n" );
document.write( "Let z = amt invested at 5%<BR>\n" );
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document.write( "\"$10,000 is to be invested in three different ways.\"<BR>\n" );
document.write( "x + y + z = 10000<BR>\n" );
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document.write( "\"One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year.\"<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "-2x + y = 0<BR>\n" );
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document.write( "\" the first year, the investments bring a return of $830.<BR>\n" );
document.write( ".08x + .09y + .05z = 830<BR>\n" );
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document.write( "From these three equations we can derive a matrix<BR>\n" );
document.write( " 1, 1, 1, 10000<BR>\n" );
document.write( "-2, 1, 0, 0<BR>\n" );
document.write( ".08, .09, .05, 830\r<BR>\n" );
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document.write( " How much was invested in each way?   </SPAN>\n" );
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