document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148351>Question 1148351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jill invested $100,000 in stocks and bonds. Equities earned a total return of<BR>\n" );
document.write( "12%, and the fixed income component earned 8%. If she had invested twice<BR>\n" );
document.write( "as much in equities, she would have made $1,800 more. How much was<BR>\n" );
document.write( "invested in equities?\r<BR>\n" );
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document.write( "I don't need the answer as much as I need to understand the steps. Your help is greatly appreciated, thank you in advance!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769737 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=769737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this one was tough, since i never saw one like this before, but i think i have it.\r<BR>\n" );
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document.write( "let x = the amount invested in stocks.<BR>\n" );
document.write( "let y = the amount invested in bonds.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x + y = 100,000<BR>\n" );
document.write( ".12 * x + .08 * y = I\r<BR>\n" );
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document.write( "I represents the interest on the investment.\r<BR>\n" );
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document.write( "if you invest twice as much in stocks, you will get I + 1800.\r<BR>\n" );
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document.write( "when you invest twice as much in stocks, the amount invested in bonds is less by the original amount invested in stocks.\r<BR>\n" );
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document.write( "you will get 2x + (y - x) = 100,000<BR>\n" );
document.write( "simplify to get 2x + y - x = 100,000<BR>\n" );
document.write( "combine like terms to get x + y = 100,000<BR>\n" );
document.write( "bottom line here is that the equation of 2x + (y-x) = 100,000 doesn't tell me anything, by itself, since i simplifies to the original equation of x + y = 100,000.\r<BR>\n" );
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document.write( "i decided not to simplify the x + y equation and left it as 2 * x + (y - x) = 100,000.\r<BR>\n" );
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document.write( "as it turns out, i didn't have to use it, since i had enough without it.\r<BR>\n" );
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document.write( "the interest equation does tell me something.\r<BR>\n" );
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document.write( "i get .12 * x + .08 * y = I for the original equation.<BR>\n" );
document.write( "i get .12 * (2 * x) + .08 * (y - x) = I + 1800 for the doubling of x equation.\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( ".24 * x + .08 * y - .08 * x = I + 1800<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( ".16 * x - .08 * y = I + 1800\r<BR>\n" );
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document.write( "there are two equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( ".12 * x + .08 * y = I<BR>\n" );
document.write( ".16 * x + .08 * y = I + 1800\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( ".04 * x = 1800<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1800 / .04 = 45,000\r<BR>\n" );
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document.write( "this means that y = 55,000\r<BR>\n" );
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document.write( "i have x = 45,000 and y = 55,000<BR>\n" );
document.write( ".12 * x + .08 * y = 9800\r<BR>\n" );
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document.write( "when i double x, i have to subtract that same amount from y.<BR>\n" );
document.write( "i get 2 * x + (y - x) = 100,000 which becomes:<BR>\n" );
document.write( "90,000 + 10,000 = 100,000<BR>\n" );
document.write( "the interest becomes:<BR>\n" );
document.write( ".12 * 90,000 + .08 * 10,000 = 11,600\r<BR>\n" );
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document.write( "the difference is 11,600 - 9,800 = 1,800.\r<BR>\n" );
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document.write( "your solution is that the original amount invested in equities is 45,000.\r<BR>\n" );
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document.write( "i have no idea if this is the preferred way to solve this, but it did work, so i'll stick with it for now.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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