document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115269>Question 1115269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Meisha has $25,000 that she wants to invest. She invests it in accounts paying 12%, 7%, and<BR>\n" );
document.write( "6% simple interest. The account paying 12% is a higher-risk account, so she wants the<BR>\n" );
document.write( "amount in that account to be half of the amount she has in the account paying 6% simple<BR>\n" );
document.write( "interest. If her annual interest is $1945, how much is 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 #853830 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53727)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Meisha has $25,000 that she wants to invest. She invests it in accounts paying 12%, 7%, <BR>\n" );
document.write( "and 6% simple interest. The account paying 12% is a higher-risk account, so she wants the<BR>\n" );
document.write( "amount in that account to be half of the amount she has in the account paying 6% simple<BR>\n" );
document.write( "interest. If her annual interest is $1945, how much is invested at each rate?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For this problem (and for many other similar problems) there is much more simpler \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and more straightforward way to solve, which I will show you right now.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Let 'x' be the amount invested at 12%.\r\n" );
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document.write( "Then the amount invested at 6% is 2x, \r\n" );
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document.write( "and the amount invested at 7% is the rest (25000 - x - 2x) = (25000-3x) dollars.\r\n" );
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document.write( "Now write an equation for the total annual interest \r\n" );
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document.write( "    0.12x + 0.06(2x) + 0.07*(25000-3x) = 1945  dollars.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    0.12x + 0.12x + 1750 - 0.21x = 1945,\r\n" );
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document.write( "    0.12x + 0.12x - 0.21x = 1945 - 1750,\r\n" );
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document.write( "             0.03x         =    195\r\n" );
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document.write( "                 x         =    195/0.03 =  6500  dollars.\r\n" );
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document.write( "Thus, $6500 was invested at 12%;  2*6500 = 13000 dollars were invested at 6% and the rest, \r\n" );
document.write( "25000-13000-6500 = $5500  were invested at 7%.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "I neither used a system of three equation nor a system of two equations.\r<BR>\n" );
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document.write( "One equation in one unknown was enough to find all three unknowns.\r<BR>\n" );
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document.write( "It is a focus-pocus, which works successfully in many other similar problems.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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