document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=236084>Question 236084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y.  The total value of Bob's holdings of these two companies is $340,000.\r<BR>\n" );
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document.write( "Suppose Frank owns 8,000 shares of Company X and 6,000 shares of Company Y.  The total value of Franks holdings of these two companies is $340,000.\r<BR>\n" );
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document.write( "a.  Write equations for Bob and Frank's holdings.  Use the variables X and Y to represent the values of shares of Company X and Company Y.\r<BR>\n" );
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document.write( "b. Solve for the value of a share of Company X and Company Y.  Show your work so you can get partial credit even if your final answer is wrong.\r<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 #173994 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=173994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Bob owns 2000*x + 10000*y = 340000<BR>\n" );
document.write( "Frank owns 8000*x + 6000*y = 340000\r<BR>\n" );
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document.write( "If we solve these equations simultaneously, then we should get the value of each share.\r<BR>\n" );
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document.write( "your equations are:\r<BR>\n" );
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document.write( "2000x + 10000y = 340000<BR>\n" );
document.write( "8000x + 6000y = 340000\r<BR>\n" );
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document.write( "there are 3 ways to solve this equation simultaneously.\r<BR>\n" );
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document.write( "1 is by substitution.<BR>\n" );
document.write( "2 is by elimination.<BR>\n" );
document.write( "3 is by setting the equations the left side of each equation equal to each other because they are both equal to 340000.\r<BR>\n" );
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document.write( "we'll use elimination.\r<BR>\n" );
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document.write( "the equations are:\r<BR>\n" );
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document.write( "2000x + 10000y = 340000 (equation 1)<BR>\n" );
document.write( "8000x + 6000y = 340000 (equation 2)\r<BR>\n" );
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document.write( "multiply the first equation by 4 to get:\r<BR>\n" );
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document.write( "8000x + 40000y = 1360000 equation 3)<BR>\n" );
document.write( "8000x + 6000y = 340000 (equation 2)\r<BR>\n" );
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document.write( "subtract equation 2 from equation 3 to get:\r<BR>\n" );
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document.write( "34000y = 1020000\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 1020000/34000 = 30\r<BR>\n" );
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document.write( "replace y with 30 in equation 1 to get:\r<BR>\n" );
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document.write( "2000x + 10000y = 340000 (equation 1) becomes:\r<BR>\n" );
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document.write( "2000x + 10000*30 = 340000 which becomes:<BR>\n" );
document.write( "2000x + 300000 = 340000<BR>\n" );
document.write( "subtract 300000 from both sides to get:<BR>\n" );
document.write( "2000x = 340000 - 300000 which becomes:<BR>\n" );
document.write( "2000x = 40000<BR>\n" );
document.write( "divide both sides by 2000 to get:<BR>\n" );
document.write( "x = 20\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 20<BR>\n" );
document.write( "y = 30\r<BR>\n" );
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document.write( "substitute in both original equations to confirm the answer is good for both equations simultaneously.\r<BR>\n" );
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document.write( "2000x + 10000y = 340000 (equation 1)<BR>\n" );
document.write( "8000x + 6000y = 340000 (equation 2)\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "2000*20 + 10000*30 = 340000<BR>\n" );
document.write( "8000*20 + 6000*30 = 340000\r<BR>\n" );
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document.write( "these become:\r<BR>\n" );
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document.write( "40000 + 300000 = 340000<BR>\n" );
document.write( "160000 + 180000 = 340000\r<BR>\n" );
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document.write( "these become:\r<BR>\n" );
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document.write( "340000 = 340000<BR>\n" );
document.write( "340000 = 340000\r<BR>\n" );
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document.write( "both equations are true which means that the answer provided are good.\r<BR>\n" );
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document.write( "your answers are:\r<BR>\n" );
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document.write( "x = 20 (each share of company x = $20.00)<BR>\n" );
document.write( "y = 30 (each share of company  y = $30.00)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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