document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768059>Question 768059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person invested $7800 for one year,part at 6%, part at 9%, and the remainder at 12%.The total annual income from these investments was $795.The amount of money invested a t 12% was $1200 more than the amounts invested at 6% and 9% combined.What was the amount invested at each rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468050 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=468050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person invested $7800 for one year,part at 6%, part at 9%, and the remainder at 12%.The total annual income from these investments was $795.The amount of money invested a t 12% was $1200 more than the amounts invested at 6% and 9% combined.What was the amount invested at each rate?\r<BR>\n" );
document.write( "\n" );
document.write( "6%--------------------x<BR>\n" );
document.write( "9%--------------------y\r<BR>\n" );
document.write( "\n" );
document.write( "12%-------------------7800-(x+y)\r<BR>\n" );
document.write( "\n" );
document.write( "TOTAL INCOME<BR>\n" );
document.write( "6%x+9%y+12%*7800-(x+y) = 795\r<BR>\n" );
document.write( "\n" );
document.write( "SECOND CONDITION\r<BR>\n" );
document.write( "\n" );
document.write( "7800-(x+y)=x+y+1200\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "6%x+9%y+12%*7800-(x+y) = 795<BR>\n" );
document.write( "multiply equation by 100<BR>\n" );
document.write( "6x+9y+12*(7800-(x+y)) =79500\r<BR>\n" );
document.write( "\n" );
document.write( "6x+9y+93600-12x-12y=79500<BR>\n" );
document.write( "-6x-3y=79500-93600<BR>\n" );
document.write( "-6x-3y=-14100<BR>\n" );
document.write( "/-3<BR>\n" );
document.write( "2x+y=4700........................(1)\r<BR>\n" );
document.write( "\n" );
document.write( "7800-(x+y)x+y+1200<BR>\n" );
document.write( "7800-x-y=x+y+1200<BR>\n" );
document.write( "2x+2y=6600<BR>\n" );
document.write( "/2<BR>\n" );
document.write( "x+y=3300...........................(2)\r<BR>\n" );
document.write( "\n" );
document.write( "solve eqn (1) & (2)\r<BR>\n" );
document.write( "\n" );
document.write( "2	x	+	1	y	=	4700	.............1	<BR>\n" );
document.write( "Total value								<BR>\n" );
document.write( "1	x	+	1	y	=	3300	.............2	<BR>\n" );
document.write( "Eliminate	y							<BR>\n" );
document.write( "multiply (1)by		-1						<BR>\n" );
document.write( "Multiply (2) by		1						<BR>\n" );
document.write( "-2	x		-1	y	=	-4700		<BR>\n" );
document.write( "1	x	+	1	y	=	3300		<BR>\n" );
document.write( "Add the two equations								<BR>\n" );
document.write( "-1	x				=	-1400		<BR>\n" );
document.write( "/	-1							<BR>\n" );
document.write( "x	=	1400						<BR>\n" );
document.write( "plug value of			x	in (1)				<BR>\n" );
document.write( "2	x	+	1	y	=	4700		<BR>\n" );
document.write( "2800		+		y	=	4700		<BR>\n" );
document.write( "				y	=	4700		-2800<BR>\n" );
document.write( "				y	=	1900		<BR>\n" );
document.write( "				y	=	1900		<BR>\n" );
document.write( "x=	1400investment at6%						<BR>\n" );
document.write( "y=	1900 investment at 9%	<BR>\n" );
document.write( "Balance at 12%					<BR>\n" );
document.write( "m.ananth@hotmail.ca								<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );