document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204859>Question 204859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a plate of WHOLE cookies; I gave Jodie half of what was on the plate, plus half of a cookie. I gave Beth half of what was left on the plate, plus half of a cookie; I gave Michelle half of what was left on the plate, plus half of a cookie. There are no cookies left, and I didn’t break any in half. How many cookies were on the plate to begin with? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154614 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=154614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, I tried 7 cookies and that seems to work, and I know that this is not an algebraic answer, but I think that it can be worked out.<BR>\n" );
document.write( "Start with 7.<BR>\n" );
document.write( "To Jodie, half of 7 is 3.5 plus 0.5 = 4 so there are 3 cookies left.<BR>\n" );
document.write( "To Beth, half of 3 is 1.5 pus 0.5 = 2, so now there is 1 cookie left.<BR>\n" );
document.write( "To Michelle, half of 1 is 0.5 plus o.5 = 1, no more cookies left and no cookies needed to be broken.<BR>\n" );
document.write( "----------------------------------------------------------------------<BR>\n" );
document.write( "How did I get 7?  Read on!<BR>\n" );
document.write( "Let x = the original number of whole cookies on the plate.<BR>\n" );
document.write( "To Jodie, you gave: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F2+%2B+1%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2F2+%2B+1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > what was left after that can be expressed by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28x%2F2%2B1%2F2%29 ALIGN=MIDDLE  ALT=\"x-%28x%2F2%2B1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > let's call this quantity y, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-%28x%2F2%2B1%2F2%29%29 ALIGN=MIDDLE  ALT=\"y+=+%28x-%28x%2F2%2B1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "To Beth, you gave:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2F2%2B1%2F2%29 ALIGN=MIDDLE  ALT=\"%28y%2F2%2B1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > what was left after that can be expressed by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28y%2F2%2B1%2F2%29 ALIGN=MIDDLE  ALT=\"y-%28y%2F2%2B1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > let's call this quantity z, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28y-%28y%2F2%29%2B1%2F2%29 ALIGN=MIDDLE  ALT=\"z+=+%28y-%28y%2F2%29%2B1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To Michelle, you gave:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2F2%2B2%2F2 ALIGN=MIDDLE  ALT=\"z%2F2%2B2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > what was left after that can be xepressed by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-%28z%2F2%2B1%2F2%29 ALIGN=MIDDLE  ALT=\"z-%28z%2F2%2B1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...and, because there were no cookies left, we'll call this zero, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-%28z%2F2%2B1%2F2%29+=+0 ALIGN=MIDDLE  ALT=\"z-%28z%2F2%2B1%2F2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we can solve this for z: First simplify it.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282z-z-1%29%2F2+=+0 ALIGN=MIDDLE  ALT=\"%282z-z-1%29%2F2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-1+=+0 ALIGN=MIDDLE  ALT=\"z-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28z+=+1%29 ALIGN=MIDDLE  ALT=\"highlight%28z+=+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we know z, we can solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%28y-%28y%2F2%2B1%2F2%29%29 ALIGN=MIDDLE  ALT=\"1+=+%28y-%28y%2F2%2B1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y-y-1%29%2F2+=+1 ALIGN=MIDDLE  ALT=\"%282y-y-1%29%2F2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1+=+2 ALIGN=MIDDLE  ALT=\"y-1+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+3%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, we can solve for x, the original number of cookies.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+%28x-%28x%2F2%2B1%2F2%29%29 ALIGN=MIDDLE  ALT=\"3+=+%28x-%28x%2F2%2B1%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-x-1%29%2F2+=+3 ALIGN=MIDDLE  ALT=\"%282x-x-1%29%2F2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=+6 ALIGN=MIDDLE  ALT=\"x-1+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+7%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );