document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230895>Question 230895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Word Problem Six - A group of people come forward to claim a $1,000,000 lottery jackpot, which the winners are to share equally.  Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by $75,000.  How many winners are there and what were their shares? (Show a complete algebraic solution for the problem and check the answer.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171039 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A group of people come forward to claim a $1,000,000 lottery jackpot, which the winners are to share equally. Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by $75,000. How many winners are there and what were their shares? <BR>\n" );
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document.write( "Let the original group size of winners be \"x\";<BR>\n" );
document.write( "The original average prize would be 1,000,000/x dollars<BR>\n" );
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document.write( "Number of winners after 3 more join is \"x+3\"<BR>\n" );
document.write( "New average prize is 1,000,000/(x+3) dollars<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "Original - New = 75000<BR>\n" );
document.write( "1,000,000/x - 1,000,000/(x+3) = 75000<BR>\n" );
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document.write( "Divide through by 75000 to get:<BR>\n" );
document.write( "13.333/x - 13.333/(x+3) = 1<BR>\n" );
document.write( "Multiply thru by x(x+3)<BR>\n" );
document.write( "(40/3)(x+3) - (40/3)x = x^2+3x<BR>\n" );
document.write( "Multiply thru by 3:<BR>\n" );
document.write( "40x + 120 - 40x = 3x^2+9x<BR>\n" );
document.write( "3x^2 + 9x -120 = 0<BR>\n" );
document.write( "x^2 + 3x - 40 = 0<BR>\n" );
document.write( "Positive Solution:<BR>\n" );
document.write( "x = [-3 + sqrt(9-4*-40)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = [-3 + sqrt(169)]/2<BR>\n" );
document.write( "x = [-3 + 13]/2<BR>\n" );
document.write( "x = 5 (original number of winners)<BR>\n" );
document.write( "x+3 = 8 (total number of winners)<BR>\n" );
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document.write( "1,000,000/8 = $125,000 (amount each winner received)<BR>\n" );
document.write( "===========================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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