document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=651623>Question 651623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the solution for the following word problem?\r<BR>\n" );
document.write( "\n" );
document.write( "An investor invested a total of $2500 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. If the investor's total profit was $65, how much was invested in each mutual fund?\r<BR>\n" );
document.write( "\n" );
document.write( "The amount invested in the mutual fund that earned 5% = ?<BR>\n" );
document.write( "The amount invested in the mutual fund that earned 2% = ?\r<BR>\n" );
document.write( "\n" );
document.write( "Work I have attempted on the problem:\r<BR>\n" );
document.write( "\n" );
document.write( "$2500/5% = $125.00 profit<BR>\n" );
document.write( "$2500/2% = $50.00 profit<BR>\n" );
document.write( "Amount invested in each mutual fund is $65/2 = $32.50 profit<BR>\n" );
document.write( "Am I on the right track? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407748 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=407748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = amount invested at 5%<BR>\n" );
document.write( "let y = amount invested at 2%<BR>\n" );
document.write( "you have 2 equations.<BR>\n" );
document.write( "x + y = 2500<BR>\n" );
document.write( ".05x + .02y = 65<BR>\n" );
document.write( "the first equation states that the total money invested is 2500.<BR>\n" );
document.write( "the second equation states that the total profit is equal to 65.<BR>\n" );
document.write( "these are 2 equations that need to be solved simultaneously.<BR>\n" );
document.write( "simples way to solve is by substitution.<BR>\n" );
document.write( "solve for y in the first equation to get:<BR>\n" );
document.write( "y = 2500 -x<BR>\n" );
document.write( "substitute that value for y in the second equation to get:<BR>\n" );
document.write( ".05x + .02(2500-x) = 65<BR>\n" );
document.write( "what you have done is reduce the problem to 1 equation in 1 unknown that can be solved easily.<BR>\n" );
document.write( "simplify that equation to get:<BR>\n" );
document.write( ".05x + .02(2500) - .02x = 65<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( ".05x + 50 - .02x = 65<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( ".03x + 50 = 65<BR>\n" );
document.write( "subtract 50 from both sides of the equation to get:<BR>\n" );
document.write( ".03x = 15<BR>\n" );
document.write( "divide both sides of the equation by .03 to get:<BR>\n" );
document.write( "x = 15/.03 = 500<BR>\n" );
document.write( "since x + y = 2500 and x = 500, the equation becomes:<BR>\n" );
document.write( "500 + y = 2500<BR>\n" );
document.write( "solve for y to get y = 2000<BR>\n" );
document.write( "you solution is x = 500 and y = 2000<BR>\n" );
document.write( "test the solution by substituting in the original equations.<BR>\n" );
document.write( "x + y becomes 500 + 2000 becomes 2500 which is equal to the total money invested so that part is good.<BR>\n" );
document.write( ".05x + .02y = 65 becomes .05(500) + .02(2000) which becomes 25 + 40 which becomes 65 which is equal to the total interest earned so that part is good.<BR>\n" );
document.write( "x = 500 and y = 2000 is your solution.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );