document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136627>Question 136627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Auggie spent all of his money in 5 stores. In each store, he spent $1 more than one-half of what he had when he went in. How many dollars did Auggie have when he entered the first store? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100053 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=100053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> He starts with x dollars, so in the first store he spends <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2%2B1 ALIGN=MIDDLE  ALT=\"x%2F2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So when he leaves the first store he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28x%2F2%2B1%29=x%2F2-1=x%2F2-2%2F2=%28x-2%29%2F2 ALIGN=MIDDLE  ALT=\"x-%28x%2F2%2B1%29=x%2F2-1=x%2F2-2%2F2=%28x-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So in the second store he spends <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%2F%282%2A2%29%29%2B1 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%2F%282%2A2%29%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%2F%282%2A2%29%29-1=%28x-2-4%29%2F4=%28x-6%29%2F4 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%2F%282%2A2%29%29-1=%28x-2-4%29%2F4=%28x-6%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > left.\r<BR>\n" );
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document.write( "And so on.\r<BR>\n" );
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document.write( "I'll leave it to you to verify that when he leaves the 5th store he has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-62%29%2F64 ALIGN=MIDDLE  ALT=\"%28x-62%29%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars remaining, and by the conditions of the problem this expression must be equal to zero (because he spent all of his money).  If  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-62%29%2F64=0 ALIGN=MIDDLE  ALT=\"%28x-62%29%2F64=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-62=0 ALIGN=MIDDLE  ALT=\"x-62=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=62 ALIGN=MIDDLE  ALT=\"x=62\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Start: 62<BR>\n" );
document.write( "Half of 62 is 31 plus 1 is 32, leaving 30<BR>\n" );
document.write( "Half of 30 is 15 plus 1 is 16, leaving 14<BR>\n" );
document.write( "Half of 14 is 7 plus 1 is 8, leaving 6<BR>\n" );
document.write( "Half of 6 is 3 plus 1 is 4, leaving 2<BR>\n" );
document.write( "Half of 2 is 1 plus 1 is 2, leaving 0  </SPAN>\n" );
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