document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912112>Question 912112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following word problem.<BR>\n" );
document.write( "Money is invested at two rates of interest.  One rate is 5% and the other is 4%.  If there is $800 more invested at 5% than at 4%, find the amount invested at each rate if the total annual interest received is $670. Let x = amount invested at 5% and y = amount invested at 4%.  Then the system that models the problem is {x = y + 800 and 0.05x + 0.04y = 670}.  Solve the system by using the method of addition. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553578 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We don't know the total invested.<BR>\n" );
document.write( "We know the difference in the two accounts.<BR>\n" );
document.write( "We know that the interest for the two accounts is $670<BR>\n" );
document.write( "0.05*x+0.04*y=670<BR>\n" );
document.write( "We know that the account at 5% has $800 more.<BR>\n" );
document.write( "x=800+y<BR>\n" );
document.write( "We substitute for x<BR>\n" );
document.write( "0.05*(800+y)+0.04*y=670<BR>\n" );
document.write( "We multiply out<BR>\n" );
document.write( "40+0.05y+0.04*y=670<BR>\n" );
document.write( "We combine like terms.<BR>\n" );
document.write( "0.09*y=630<BR>\n" );
document.write( "Isolate y<BR>\n" );
document.write( "y=$7000 at 4%<BR>\n" );
document.write( "x=800+y<BR>\n" );
document.write( "Calculate x<BR>\n" );
document.write( "x=$7800 at 5%<BR>\n" );
document.write( "Now,we know the total invested is: 14800<BR>\n" );
document.write( "Total invested $7800+$7000=$14800<BR>\n" );
document.write( "We check<BR>\n" );
document.write( "0.05*7800+0.04*7000=670<BR>\n" );
document.write( "390+280=670<BR>\n" );
document.write( "670=670<BR>\n" );
document.write( "Since this statement is TRUE and neither x nor y is negative all is well.<BR>\n" );
document.write( "codeintmt\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But you want it solved using elimination or addition\r<BR>\n" );
document.write( "\n" );
document.write( "0.05*x+0.04*y=670<BR>\n" );
document.write( "x=800+y<BR>\n" );
document.write( "x-y=800<BR>\n" );
document.write( "0.05*x+0.04*y=670<BR>\n" );
document.write( "multiply by 100 <BR>\n" );
document.write( "5*x+4*y=67000<BR>\n" );
document.write( "x-y=800<BR>\n" );
document.write( "multiply by 6<BR>\n" );
document.write( "4x-4y=3200<BR>\n" );
document.write( "5*x+4*y=67000<BR>\n" );
document.write( "add<BR>\n" );
document.write( "9x=70200<BR>\n" );
document.write( "x=7800 at 5%<BR>\n" );
document.write( "y=7000 at 4% </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );