document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=929300>Question 929300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this problem?\r<BR>\n" );
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document.write( "Suppose that it takes 927 digits to number the pages of a book beginning with page 1 and ending with the last page of text. How many numbered pages are contained in this book? Your answer must include a method of solution and please state your answer in a sentence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #564234 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=564234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE FIFTH-GRADER SOLUTION:<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > pages with page number < 10,<BR>\n" );
document.write( "and it takes only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit/character to print each page number for those pages,<BR>\n" );
document.write( "for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A1=9 ALIGN=MIDDLE  ALT=\"9%2A1=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits/characters to number those pages.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99 ALIGN=MIDDLE  ALT=\"99\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so there will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99 ALIGN=MIDDLE  ALT=\"99\"   DISABLED_style= \"max-width:90%; height:auto;\" > pages with one-digit or two-digit page numbers.<BR>\n" );
document.write( "Nine <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%29 ALIGN=MIDDLE  ALT=\"%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of those pages have one-digit numbers, but the remaining<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99-9=90 ALIGN=MIDDLE  ALT=\"99-9=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > of those pages have two-digit page numbers.<BR>\n" );
document.write( "As it takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits/characters to print the each page number for those pages,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2A2=180 ALIGN=MIDDLE  ALT=\"90%2A2=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits/characters will be used to number the pages with two-digit numbers.<BR>\n" );
document.write( "So far, to number pages 1 through 99, we have used <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B180=189 ALIGN=MIDDLE  ALT=\"9%2B180=189\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits/characters .<BR>\n" );
document.write( "For most books, after page 99, all the other pages have 3-digit numbers,<BR>\n" );
document.write( "and it takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits/characters to print the each page number for those pages.<BR>\n" );
document.write( "If the book has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > pages, there will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99 ALIGN=MIDDLE  ALT=\"99\"   DISABLED_style= \"max-width:90%; height:auto;\" > pages with one-digit or two-digit page numbers.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C1000 ALIGN=MIDDLE  ALT=\"x%3C1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-99 ALIGN=MIDDLE  ALT=\"x-99\"   DISABLED_style= \"max-width:90%; height:auto;\" > pages will have 3-digit page numbers, and we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=927-189=738 ALIGN=MIDDLE  ALT=\"927-189=738\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits/characters left to print the 3-digit page numbers on those pages.<BR>\n" );
document.write( "At 3 digits per page, we can number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=738%2F3=246 ALIGN=MIDDLE  ALT=\"738%2F3=246\"   DISABLED_style= \"max-width:90%; height:auto;\" > such pages.<BR>\n" );
document.write( "After that we will have numbered all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B180%2B246=highlight%28345%29 ALIGN=MIDDLE  ALT=\"9%2B180%2B246=highlight%28345%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > pages of the book.<BR>\n" );
document.write( " <BR>\n" );
document.write( "TO SHOW OFF YOUR ALGEBRA SKILLS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A1%2B%2899-9%29%2A2%2B%28x-99%29%2A3=927 ALIGN=MIDDLE  ALT=\"9%2A1%2B%2899-9%29%2A2%2B%28x-99%29%2A3=927\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2B90%2A2%2B%28x-99%29%2A3=927 ALIGN=MIDDLE  ALT=\"90%2B90%2A2%2B%28x-99%29%2A3=927\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2B180%2B%28x-99%29%2A3=927 ALIGN=MIDDLE  ALT=\"90%2B180%2B%28x-99%29%2A3=927\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=189%2B%28x-99%29%2A3=927 ALIGN=MIDDLE  ALT=\"189%2B%28x-99%29%2A3=927\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-99%29%2A3=927-189 ALIGN=MIDDLE  ALT=\"%28x-99%29%2A3=927-189\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-99%29%2A3=738 ALIGN=MIDDLE  ALT=\"%28x-99%29%2A3=738\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-99=738%2F3 ALIGN=MIDDLE  ALT=\"x-99=738%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=246%2B99 ALIGN=MIDDLE  ALT=\"x=246%2B99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=highlight%28345%29 ALIGN=MIDDLE  ALT=\"x=highlight%28345%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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