document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=841563>Question 841563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sandra invested $8000 in two mutual funds. At the end of the year, the percent return on one fund (x) was 8% and the percent return on the other fund (y) was 3%. The combined return on both funds was $345. Which system of equations can be used to find how much Sandra invested in each fund? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #507012 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=507012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 2 equations to work with.<BR>\n" );
document.write( "x + y = 8000 is your first equation.<BR>\n" );
document.write( ".08x + .03y = 345 is your second equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you solve these equations simultaneously for x and y to get your answer.<BR>\n" );
document.write( "you can do it by substitution or elimination.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'll do it by elimination.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 8000<BR>\n" );
document.write( ".08x + .03y = 345\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the second equation by -12.5 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 8000<BR>\n" );
document.write( "-x - .375y = -4312.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add the 2 equations together to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y - .375y = 8000 - 4312.5<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( ".625y = 3687.5<BR>\n" );
document.write( "divide both sides of this equation by .625 to get:<BR>\n" );
document.write( "y = 3687.5/.625 = 5900\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x + y = 8000, then x must be equal to 2100 because 5900 and 2100 = 8000.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so you now have:<BR>\n" );
document.write( "x = 2100 and y = 5900.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take .08 * 2100 and add it to .03 * 5900 to get 345.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "numbers check out and your solution is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also solve it by substitution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 8000<BR>\n" );
document.write( ".08x + .03y = 345\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x in the first equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 8000 - y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute for x in the second equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".08(8000 - y) + .03y = 345\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "640 - .08y + .03y = 345\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "640 - .05y = 345\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 345 from both sides of this equation and add .05y to both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "640 - 345 = .05y<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "295 = .05y<BR>\n" );
document.write( "divide both sides of this equation by .05 to get:<BR>\n" );
document.write( "y = 5900\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answer will be the same as the one you got through elimination.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also solve by graphing although the solution you get using that method may not be as exact.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graphical solution is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1000%2C10000%2C-1000%2C10000%2C%288000-x%29%2C%28345-.08x%29%2F.03%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1000%2C10000%2C-1000%2C10000%2C%288000-x%29%2C%28345-.08x%29%2F.03%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the intersection point is the solution.<BR>\n" );
document.write( "it's not easy to see, but i did  verify with an other graphing calculator that it is x = 2100 and y = 5900.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );