document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168300>Question 1168300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using a graphing calculator how would you set up the solution to the following word problem:<BR>\n" );
document.write( "Suppose you have received a total of $1,520 a year in interest from three investments. The interest rates for the investments are 5%, 7%, and 8%. The amount is invested at 5% is half of the amount invested at 7%. The amount invested at 7% is $1,500 less than the amount invested at 8% Find the amount of money 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 #792926 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=792926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is 1520 = .05 * x + .07 * y + .08 * z\r<BR>\n" );
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document.write( "x is the amount invested at 5%<BR>\n" );
document.write( "y is the amount invested at 7%<BR>\n" );
document.write( "z is the amount invested at 8%.\r<BR>\n" );
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document.write( "you are given that the amount invested at 5% is half the amount invested at 7%.\r<BR>\n" );
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document.write( "this makes x = .5 * y.\r<BR>\n" );
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document.write( "you are given that the amount invested at 7% is 1500 less than the amount invested at 8%.\r<BR>\n" );
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document.write( "this makes y = z - 1500.\r<BR>\n" );
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document.write( "solve for z in the equation of y = z - 1500 to get z = y + 1500.\r<BR>\n" );
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document.write( "you have x = .5 * y and z = y + 1500.\r<BR>\n" );
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document.write( "in the equation of 1520 = .05 * x + .07 * y + .08 * z, replace x with .5 * y and replace z with y + 1500 to get:\r<BR>\n" );
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document.write( "1520 = .05 * .5 * y + .07 * y + .08 * (y + 1500)\r<BR>\n" );
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document.write( "simplify to get 1520 = .025 * y + .07 * y + .08 * y + .08 * 1500\r<BR>\n" );
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document.write( "since .08 * 1500 = 120, then the equation becomes:\r<BR>\n" );
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document.write( "1520 = .025 * y + .07 * y + .08 * y + 120\r<BR>\n" );
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document.write( "subtract 120 from both sides of the equation to get:\r<BR>\n" );
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document.write( "1520 - 120 = .025 * y + .07 * y + .08 * y\r<BR>\n" );
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document.write( "simplify and combine like terms to get:\r<BR>\n" );
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document.write( "1400 = .175 * y\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 8000.\r<BR>\n" );
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document.write( "when y = 8000, x = .5 * y = 4000 and z = y + 1500 = 9500\r<BR>\n" );
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document.write( "you get x = 4000, y = 8000, z = 9500\r<BR>\n" );
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document.write( "your original equation of 1520 = .05 * x + .07 * y + .08 * z becomes:\r<BR>\n" );
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document.write( "1520 = .05 * 4000 + .07 * 8000 + .08 * 9500\r<BR>\n" );
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document.write( "simplify to get 1520 = 1520.\r<BR>\n" );
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document.write( "this confirms the values of x and y and z are good.\r<BR>\n" );
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document.write( "the amount invested at 5% is 4000<BR>\n" );
document.write( "the amount invested at 7% is 8000<BR>\n" );
document.write( "the amount invested at 8% is 9500\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "the amount invested at 5% is half the amount invested at 7%.<BR>\n" );
document.write( "the amount invested at 7% is 1500 less than the amount invested at 8%.\r<BR>\n" );
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document.write( "the requirements of the problem have been satisfied, so the solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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