document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039073>Question 1039073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here's my question:<BR>\n" );
document.write( "Mrs. Pasternak invested $100,000 in two different healthcare companies.  The first earned a 6% profit, and the second earned a 12% profit.  If Mrs. Pasternak made 2 times as much profit from the 12% investment as she did from the 6% investment, how much did she invest in the company that made 6%?<BR>\n" );
document.write( "I think it's set up like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%280.06%29%2B%282x%29%280.12%29=100%2C000 ALIGN=MIDDLE  ALT=\"%28x%29%280.06%29%2B%282x%29%280.12%29=100%2C000\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Is this right?  If not, how should I do it?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653800 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=653800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i would say she invested 50,000 in each.<BR>\n" );
document.write( "the reason is that 12% is two times 6%, so if she made twice as much profit from the 12% investment as she made from the 6% investment, she had to invest the same amount in each.\r<BR>\n" );
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document.write( "50,000 * .06 = 3000<BR>\n" );
document.write( "50,000 * .12 = 6000\r<BR>\n" );
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document.write( "you can also solve this algebraically as follows:\r<BR>\n" );
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document.write( "x = the 6% investment<BR>\n" );
document.write( "y = the 12% investment<BR>\n" );
document.write( "p = profit\r<BR>\n" );
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document.write( "x + y = 100,000<BR>\n" );
document.write( ".06x + .12y = p\r<BR>\n" );
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document.write( "you are given that the profit from the 12% investment is twice the profit from the 6% investment.\r<BR>\n" );
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document.write( "the equation for that is .12 * y = 2 * .06 * x\r<BR>\n" );
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document.write( "simplify this equation to get .12 * y = .12 * x<BR>\n" );
document.write( "solve for y to get y = .12 * x / .12<BR>\n" );
document.write( "simplify to get y = x.\r<BR>\n" );
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document.write( "in the equation of x + y = 100,000, replace y with x to get x + x = 100,000.<BR>\n" );
document.write( "simplify to get 2*x = 100,000<BR>\n" );
document.write( "divide both sides of the equation by 2 to get x = 50,000\r<BR>\n" );
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document.write( "since x = 50,000, then y must also be equal to 50,000.\r<BR>\n" );
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document.write( "the profit equation of .06 * x + .12 * y = p becomes .06 * 50,000 + .12 * 50,000 = p\r<BR>\n" );
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document.write( "simplify to get 3000 + 6000 = p\r<BR>\n" );
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document.write( "p is equal to 9000.\r<BR>\n" );
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document.write( "the profit on the 12% investment is twice the profit on the 6% investment.\r<BR>\n" );
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document.write( "my intuition up front was ok and the algebra supported it.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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