document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019123>Question 1019123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can $45,000 be invested part at 10% annual simple interest and the remainder of 5% annual simple interest so that the interest earned by the two accounts will be equal the amount to invest 10% is? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635221 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=635221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it can't.\r<BR>\n" );
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document.write( "if the first part is invested at 10% and the second part is invested at 5%, the composite interest rate will be less than 10% unless the part that is invested at 5% is equal to 0.\r<BR>\n" );
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document.write( "you want a composite interest rate of 10%.<BR>\n" );
document.write( "you invest x at 10%.<BR>\n" );
document.write( "you invest y at 5%.\r<BR>\n" );
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document.write( "x + y = 45,000\r<BR>\n" );
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document.write( ".10*x + .05*y = .10 * (x + y)\r<BR>\n" );
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document.write( "simplify to get .10*x + .05*y = .10*x + .10*y\r<BR>\n" );
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document.write( "subtract .10*x and .10*y from both sides of the equation to get:\r<BR>\n" );
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document.write( ".10*x + .05*y - .10*x - .10*y = 0\r<BR>\n" );
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document.write( "combine like terms to get -.05*y = 0\r<BR>\n" );
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document.write( "solve fory to get y = 0.\r<BR>\n" );
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document.write( "since x + y = 45,000, and y = 0, then x must be equal to 45,000.\r<BR>\n" );
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document.write( "you must invest 0 at 5% and 45,000 at 10% to get a total of 45,000 at 10%.\r<BR>\n" );
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document.write( "so, the problem you posed is wrong because, in order for it to work, one of the parts must be greater than 10% and one of the parts must be less than 10%.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume the first part is invested at 20% and the second part at 5% and you want the total to be invested at 10%.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x + y = 45,000<BR>\n" );
document.write( ".20 * x + .05 * y = .10 * (x + y)\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( ".20 * x + .05 * y = .10 * x + .10 * y\r<BR>\n" );
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document.write( "subtract .10 * x and .10 * y from both sides of the equation to get:\r<BR>\n" );
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document.write( ".20 * x + .05 * y - .10 * x - .10 * y = 0\r<BR>\n" );
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document.write( "combine like terms to get .10 * x - .05 * y = 0\r<BR>\n" );
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document.write( "from x + y = 45,000, solve for y to get y = 45,000 - x\r<BR>\n" );
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document.write( "replace y with 45,000 - x in the equationn of .10 * x - .05 * y = 0 to get:\r<BR>\n" );
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document.write( ".10 * x - .05 * (45,000 - x) = 0\r<BR>\n" );
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document.write( "simplify to get .10 * x - 2250 + .05 * x = 0\r<BR>\n" );
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document.write( "combine like terms to get .15 * x - 2250 = 0\r<BR>\n" );
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document.write( "add 2250 to both sides to get .15 * x = 2250\r<BR>\n" );
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document.write( "divide both sides by .15 to get x = 2250/.15 = 15,000\r<BR>\n" );
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document.write( "since x + y = 45,000, then y = 45000 - 15000 = 30,000\r<BR>\n" );
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document.write( "you have 15,000 invested at 20% and 30,000 invested at 5%.\r<BR>\n" );
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document.write( "your total interest will be 3000 + 1500 = 4500.\r<BR>\n" );
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document.write( "4500 / 45,000 = 10%.\r<BR>\n" );
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document.write( "it works, but only if x is invested at greater than 10% and y is invested at less than 10%.\r<BR>\n" );
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