document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10300>Question 10300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary bought some donuts.  She gave 1/2 her donuts and 1/2 a donut to her mom.  Then she gave away 1/2 her remaining donuts and 1/2 a donut to her aunt.  Then she gave 1/2 of her remaining donuts and 1/2 a donut to her sister, Kathy.  This left her with 1/4 of a dozen donuts.  How many doughnuts had she bought?\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 #5446 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's work this one backwards:\r<BR>\n" );
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document.write( "Mary ends up with 3 donuts after giving half of them and a half a donut to her sister Kathy.  This means that before giving donuts to her sister Kathy, Mary must have had 7 donuts (of the 7 donuts, she gave half of them--3 1/2--plus a half, which would be 4 donuts to her sister, leaving her with 3 donuts for herself!)\r<BR>\n" );
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document.write( "Now, this means that she ended up with 7 donuts after giving half of them plus a half donut to her aunt.  By the same thinking, she must have had 15 donuts before giving 8 donuts to her aunt (7 1/2 + 1/2), leaving 7 for herself.\r<BR>\n" );
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document.write( "So, if she ended up with 15 donuts after giving half plus a half a donut to her mother, she must have started out with 31 donuts.\r<BR>\n" );
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document.write( "Now check it by seeing if it works:\r<BR>\n" );
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document.write( "Mary started with 31 donuts (half would be 15 1/2, + 1/2 means that she gave 16 to her mother), which leaves her with 15.  She gave 7 1/2 + 1/2 or 8 to her aunt, leaving her with 7 donuts.  She gave 3 1/2 + 1/2 or 4 to her sister, leavning her with  3 donuts or 1/4 of a dozen.  \r<BR>\n" );
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document.write( "Do you think there is a math formula for this?  Did you notice that at each step of the problem, each time she had donuts left, it was 1 less than a power of 2?  She started with 31 ( 32 -1), went down to 15 (16-1), then to 7 (8-1), and 3 (4-1).  Interesting problem.  Probably some high powered math here!!\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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