document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047264>Question 1047264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Matthew makes 33 cookies and gives each friend the same number of cookies. Matthew, being selfless, takes two fewer for  himself assuming all the cookies are given out how many friends does Matthew have ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662774 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=662774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Now that you have finally stated the problem correctly, we can find a correct solution.\r<BR>\n" );
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document.write( "The fact that Matthew took two fewer cookies for himself means that if he had started with two more cookies, he could have split them evenly between himself and his friends.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> represent the number of friends and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the number of cookies each receives, we can state:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (n\ +\ 1)x\ =\ 35\">.\r<BR>\n" );
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document.write( "Since both <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> must be integers (Matthew doesn't have fractional parts of friends and the problem implies whole numbers of cookies were distributed), and the prime factorization of 35 is 5 times 7, the number of friends must be either 4 or 6 and the number of cookies given to each of the friends must be either 7 or 5.\r<BR>\n" );
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document.write( "If there are 4 friends, and each gets 7 cookies, that makes 28 cookies distributed to friends, plus the two fewer cookies (5) that Matt keeps, makes 33.\r<BR>\n" );
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document.write( "If there are 6 friends, and each gets 5 cookies, that makes 30 cookies distributed to friends, plus the two fewer cookies (3) that Matt keeps, makes 33.\r<BR>\n" );
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document.write( "Hence, Matt either has 4 friends or 6 friends.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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