document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284834>Question 284834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose tom owns 2,000 shares of company X and 10,000 shares of company Y. The total value of tom's holdings of these two companies is $372,000.<BR>\n" );
document.write( "Suppose tim owns 8,000 shares of company X and 6,000 of company Y. total value holdings is $400,000<BR>\n" );
document.write( " write an equation for tom and tim's holdings. use variables X and Y to represent the value of shares of company X and company Y then need to show the value of share of company X and Y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206623 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=206623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tom owns 2,000 shares of company X and 10,000 shares of company Y for a total value equal to $372,000.\r<BR>\n" );
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document.write( "Tim owns 8,000 shares of company X and 6,000 shares of company Y for a total value equal to $400,000.\r<BR>\n" );
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document.write( "Let a equal the value of each share of company X.\r<BR>\n" );
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document.write( "Let b equal the value of each share of company Y.\r<BR>\n" );
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document.write( "For Tom:\r<BR>\n" );
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document.write( "2,000 * a + 10,000 * b = 372,000.\r<BR>\n" );
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document.write( "For Tim:\r<BR>\n" );
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document.write( "8,000 * a + 6,000 * b = 400,000.\r<BR>\n" );
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document.write( "Since the value of each share in company X and company Y is the same, then a and b must be the same values in both equations.\r<BR>\n" );
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document.write( "To find that value, solve the 2 equations simultaneously.\r<BR>\n" );
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document.write( "The 2 equations that need to be solved simultaneously are:\r<BR>\n" );
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document.write( "2,000 * a + 10,000 * b = 372,000.<BR>\n" );
document.write( "8,000 * a + 6,000 * b = 400,000.\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( "8,000 * a + 40,000 * b = 1,488,000.<BR>\n" );
document.write( "8,000 * a + 6,000 * b = 400,000\r<BR>\n" );
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document.write( "Subtract second equation from first equation to get:\r<BR>\n" );
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document.write( "34,000 * b = 1,088,000\r<BR>\n" );
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document.write( "Divide both sides of this equation by 44,000 to get:\r<BR>\n" );
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document.write( "b = 32 dollars per share.\r<BR>\n" );
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document.write( "Substitute for b in the first original equation to get:\r<BR>\n" );
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document.write( "2,000 * a + 10,000 * b = 372,000 becomes:\r<BR>\n" );
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document.write( "2,000 * a + 10,000 * 32 = 372,000\r<BR>\n" );
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document.write( "Solve for a to get:\r<BR>\n" );
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document.write( "a = 26 dollars per share.\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "a = 26 dollars per share.<BR>\n" );
document.write( "b = 32 dollars per share.\r<BR>\n" );
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document.write( "Substitute in both original equations to get:\r<BR>\n" );
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document.write( "2,000 * a + 10,000 * b = 372,000.<BR>\n" );
document.write( "8,000 * a + 6,000 * b = 400,000.\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "2,000 * 26 + 10,000 * 32 = 52,000 + 320,000 = 372,000.<BR>\n" );
document.write( "8,000 * 26 + 6,000 * 32 = 208,000 + 192,000 = 400,000.\r<BR>\n" );
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document.write( "Since the sum of the parts is equal to the original whole, this confirms the values are good.\r<BR>\n" );
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document.write( "Your answer is:\r<BR>\n" );
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document.write( "The value of the shares of company X is $26.00 per share.\r<BR>\n" );
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document.write( "The value fo the shares of company Y is $32.00 per share.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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