document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=457415>Question 457415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP ASAP!<BR>\n" );
document.write( "Solve the following problem by setting up and solving a system of three linear equations in three variables. <BR>\n" );
document.write( "Part of $2,000 is invested at 12%, another part at 13%, and the remainder at 14%. The total yearly income from the three investments is $268. The sum of the amounts invested at 12% and 13% equals the amount invested at 14%. Determine how much is invested at each rate. <BR>\n" );
document.write( "12% interest =$?<BR>\n" );
document.write( "13% interest =$? <BR>\n" );
document.write( "14% interest =$? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313889 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=313889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 12%------------x<BR>\n" );
document.write( "13%------------y<BR>\n" );
document.write( "14%------------z\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x+y+z=2000--------------1<BR>\n" );
document.write( "12x+13y+14z=268*100--------------2<BR>\n" );
document.write( "x+y-z=0	--------------3<BR>\n" );
document.write( "																<BR>\n" );
document.write( "consider equation 1 &2	Eliminate y												<BR>\n" );
document.write( "Multiply 1 by	-13									<BR>\n" );
document.write( "Multiply 2 by	1									<BR>\n" );
document.write( "we get																<BR>\n" );
document.write( "-13x -13y-13z=	-26000						<BR>\n" );
document.write( "12x+13y+14z=26800						<BR>\n" );
document.write( "Add the two 																<BR>\n" );
document.write( "-x+z=	800	-------------4	<BR>\n" );
document.write( "consider equation 2 & 3				Eliminate y		<BR>\n" );
document.write( "-1x=800						<BR>\n" );
document.write( "Multiply 2 by	x=-800							<BR>\n" );
document.write( "Multiply 3 by-13	<BR>\n" );
document.write( "we get 																<BR>\n" );
document.write( "12x+13y+14z=26800							<BR>\n" );
document.write( "-13x-13y+13z=0							<BR>\n" );
document.write( "Add the two 																<BR>\n" );
document.write( "-1x+27z=26800	-------------5				5		<BR>\n" );
document.write( "Consider (4) & (5)			Eliminate x													<BR>\n" );
document.write( "Multiply 4 by				-1												<BR>\n" );
document.write( "Multiply (5) by				1												<BR>\n" );
document.write( "we get																<BR>\n" );
document.write( "x-z=-800										<BR>\n" );
document.write( "-x+27z=	26800										<BR>\n" );
document.write( "Add the two 																<BR>\n" );
document.write( "26z=26000										<BR>\n" );
document.write( "/26															<BR>\n" );
document.write( "z=1000----14%								<BR>\n" );
document.write( "Plug the value of z in						5										<BR>\n" );
document.write( "-x+27000=26800										<BR>\n" );
document.write( "-x=-200													<BR>\n" );
document.write( "x=200----12%													<BR>\n" );
document.write( "plug value of x & z in					1											<BR>\n" );
document.write( "200+y+1000=2000									<BR>\n" );
document.write( "y=-200+	-1000+	2000									<BR>\n" );
document.write( "y=800----13%													<BR>\n" );
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