document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158944>Question 1158944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bank loaned out $13,500, part of it at the rate of 9% annual interest, and the rest at 13% annual interest. The total interest earned for both loans was $1,635.00. How much was loaned 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 #782021 by </B><A HREF=/tutors/aboutme.mpl?userid=Amily_2190><B>Amily_2190(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Amily_2190><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets say that <BR>\n" );
document.write( "x= amount loaned at the rate of 9% annual interest<BR>\n" );
document.write( "y=amount loaned at the rate of 13% annual interest<BR>\n" );
document.write( "The two loans add up to $13,500, so this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=%2413500 ALIGN=MIDDLE  ALT=\"x%2By=%2413500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=13,500-y<BR>\n" );
document.write( "y=13,500-x\r<BR>\n" );
document.write( "\n" );
document.write( "You know how much the annual rate of interest is for each loan and the total interest that is earned, so you can create this equation:<BR>\n" );
document.write( "($13,500-y)(.09)+($13,500-x)(.13)=$1,635\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, we need to solve for x and y.<BR>\n" );
document.write( "-First, distribute the second equation to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1215-.09y%2B1755-.13x=1%2C635 ALIGN=MIDDLE  ALT=\"1215-.09y%2B1755-.13x=1%2C635\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.09y-.13x=-1335 ALIGN=MIDDLE  ALT=\"-.09y-.13x=-1335\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Equation 1......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=%2413%2C500 ALIGN=MIDDLE  ALT=\"x%2By=%2413%2C500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.09y-.13x=-1335 ALIGN=MIDDLE  ALT=\"-.09y-.13x=-1335\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that you have two equations, use elimination. Multiply the first equation by .09 to cancel out the y values.<BR>\n" );
document.write( "(.09)(x+y)=(.09)(13,500)<BR>\n" );
document.write( ".09x+.09y=1215....(Add this to the second equation)\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( ".09x+.09y=1215<BR>\n" );
document.write( "+(-.09y-.13x=-1335)<BR>\n" );
document.write( "-0.04x=-120<BR>\n" );
document.write( "x=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%243000 ALIGN=MIDDLE  ALT=\"%243000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now substitute x back into the first equation to find Y<BR>\n" );
document.write( "x+y=13,500<BR>\n" );
document.write( "3,000+y=13,500<BR>\n" );
document.write( "y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2410500 ALIGN=MIDDLE  ALT=\"%2410500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: A bank loaned $3000 at the rate of 9% annual interest and $10500 at 13% annual interest.\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helped!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );