document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360631>Question 360631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. and Mrs. Wise put $6000 into three different investments paying 9.5%, 8.5% and 6.25%, respectively. The total simple annual cost at the end of 2 years was $970. The average of the amounts invested at 9.5% and 8.5% was equal to the amount invested at 6.25%. How much was invested at each rate?\r<BR>\n" );
document.write( "\n" );
document.write( "I'm having trouble setting up the third equation (the one from \"The total simple annual cost at the end of 2 years was $970.)\r<BR>\n" );
document.write( "\n" );
document.write( "I got:\r<BR>\n" );
document.write( "\n" );
document.write( "x+y+z=6000\r<BR>\n" );
document.write( "\n" );
document.write( "and \r<BR>\n" );
document.write( "\n" );
document.write( "x+y-z=0\r<BR>\n" );
document.write( "\n" );
document.write( "for the third one I got \r<BR>\n" );
document.write( "\n" );
document.write( "19x+17y+12.5z=970<BR>\n" );
document.write( "(I multiplied 9.5, 8.5, and 6.25 by 2)<BR>\n" );
document.write( "but when I solved I got a negative number for x\r<BR>\n" );
document.write( "\n" );
document.write( "what am I doing wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257367 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=257367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mr. and Mrs. Wise put $6000 into three different investments paying 9.5%, 8.5% and 6.25%, respectively. <BR>\n" );
document.write( "The total simple annual cost at the end of 2 years was $970. <BR>\n" );
document.write( "The average of the amounts invested at 9.5% and 8.5% was equal to the amount invested at 6.25%. How much was invested at each rate? <BR>\n" );
document.write( "I'm having trouble setting up the third equation (the one from \"The total simple annual cost at the end of 2 years was $970.)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "I got: <BR>\n" );
document.write( "x+y+z=6000 <BR>\n" );
document.write( "and <BR>\n" );
document.write( "x+y-z=0 <BR>\n" );
document.write( "for the third one I got <BR>\n" );
document.write( "19x+17y+12.5z=970<BR>\n" );
document.write( "(I multiplied 9.5, 8.5, and 6.25 by 2)<BR>\n" );
document.write( "but when I solved I got a negative number for x <BR>\n" );
document.write( "what am I doing wrong?<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "x = amount at 9.5%<BR>\n" );
document.write( "y = amount at 8.5%<BR>\n" );
document.write( "z = amount at 6.25%<BR>\n" );
document.write( "x + y + z = 6000<BR>\n" );
document.write( "0.19x + 0.17y + 0.125z = 970<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "The average of the amounts invested at 9.5% and 8.5% was equal to the amount invested at 6.25%.<BR>\n" );
document.write( "(x+y)/2 = z<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "x + y + z = 6000<BR>\n" );
document.write( "x + y -2z = 0  (This one is different)<BR>\n" );
document.write( "38x+34y+25z = 194000<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Sub for z<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "x + y + (x+y)/2 = 6000<BR>\n" );
document.write( "3x + 3y = 12000<BR>\n" );
document.write( "38x+34y+25(x+y)/2 = 194000<BR>\n" );
document.write( "101x+93y = 388000<BR>\n" );
document.write( "93x +93y = 372000<BR>\n" );
document.write( "------------------ Subtract<BR>\n" );
document.write( "8x = 16000<BR>\n" );
document.write( "x = 2000<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "y = 2000<BR>\n" );
document.write( "z = 2000 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );