document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009968>Question 1009968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: An investment of $50,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total Interest from the investments was $3960. The interest from the first investment was 2 times the interest from the second. Find the amounts of the three parts of the investment. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625643 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=625643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = amount invested at 8%.<BR>\n" );
document.write( "y = amount invested at 6%.<BR>\n" );
document.write( "z = amount invested at 9%.\r<BR>\n" );
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document.write( "x + y + z = 50,000\r<BR>\n" );
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document.write( ".08x + .06y + .09z = 3960\r<BR>\n" );
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document.write( "interest on the first investment is equal to 2 times interest on the second investment.\r<BR>\n" );
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document.write( ".08x = 2 * .06y\r<BR>\n" );
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document.write( "simplify to get .08x = .12y\r<BR>\n" );
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document.write( "solve for x to get x = .12y/.08 = 1.5y\r<BR>\n" );
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document.write( "since .08x = .12y, you can replace .08x with .12y.\r<BR>\n" );
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document.write( "since x = 1.5y, you can replace x with 1.5y\r<BR>\n" );
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document.write( "your two equations of x + y + z = 50,000 and .08x + .06y + .09z = 3960 become:\r<BR>\n" );
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document.write( "1.5y + y + z = 50,000<BR>\n" );
document.write( ".12y + .06y + .09z = 3960\r<BR>\n" );
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document.write( "combine like terms in both equations to get:\r<BR>\n" );
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document.write( "2.5y + z = 50,000<BR>\n" );
document.write( ".18y + .09z = 3960\r<BR>\n" );
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document.write( "you now have 2 equations with 2 unknown variables which can be solved simultaneously for a unique solution.\r<BR>\n" );
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document.write( "we will eliminate the z variable from the 2 equations in the following manner.\r<BR>\n" );
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document.write( "multiply both sides of the first eqution by 9 and multiply both sides of the second equation by 100.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "2.5y + z = 50,000 becomes 22.5y + 9z = 450,000.<BR>\n" );
document.write( ".18y + .09z = 3960 becomes 18y + 9z = 396,000.\r<BR>\n" );
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document.write( "the 2 equations are now:\r<BR>\n" );
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document.write( "22.5y + 9z = 450,000<BR>\n" );
document.write( "18y + 9z = 396,000\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "4.5y = 54,000\r<BR>\n" );
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document.write( "divide both sides of this equation by 4.5 to get:\r<BR>\n" );
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document.write( "y = 12,000\r<BR>\n" );
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document.write( "since x = 1.5y, then x must be equal to 18,000\r<BR>\n" );
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document.write( "since x + y + z = 50,000, then z must be equal to 20,000\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 18,000<BR>\n" );
document.write( "y = 12,000<BR>\n" );
document.write( "z = 20,000\r<BR>\n" );
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document.write( "the interest on each of these investments is:\r<BR>\n" );
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document.write( ".08 * 18,000 = 1,440<BR>\n" );
document.write( ".06 * 12,000 = 720<BR>\n" );
document.write( ".09 * 20,000 = 1,800\r<BR>\n" );
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document.write( "add up the investments and you get 50,000<BR>\n" );
document.write( "add up the interest and you get 3,960\r<BR>\n" );
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document.write( "the interest on the first investment is 2 times the interest on the second investment because 1,440 = 2 * 720.\r<BR>\n" );
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document.write( "all results are confirmed as good.\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "18,000 is invested at 8%.<BR>\n" );
document.write( "12,000 is invested at 6%.<BR>\n" );
document.write( "20,000 is invested at 9%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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