document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165396>Question 165396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose students arrive at school in groups. You are the first to arrive, and you are alone, but still considered a group. The second group to arrive has two more people in it that were in your group. The third group of students to arrive has two more people in it than were in the second group. If there are 2250 kids at your school on this day, how many groups will arrive at school, assuming they all meet the requirement of having two more members than the group before them? All groups except the last one must meet the \"two more than the last group\" requirement. Write an explanation how you got to your answer and write a general statement that would fit this situation no matter how many students were in the school. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121901 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first group is one person here is a list of<BR>\n" );
document.write( "group numbers and number of people in group. Any<BR>\n" );
document.write( "group has 2 more than the previous group<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "1 --- 1<BR>\n" );
document.write( "2 --- 3<BR>\n" );
document.write( "3 --- 5<BR>\n" );
document.write( "4 --- 7<BR>\n" );
document.write( "5 --- 9<BR>\n" );
document.write( "6 --- 11<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Now here is a list of group numbers and total of people so far<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "1 --- 1<BR>\n" );
document.write( "2 --- 1 + 3 = 4<BR>\n" );
document.write( "3 --- 5 + 5 = 9<BR>\n" );
document.write( "4 --- 9 + 7 = 16<BR>\n" );
document.write( "5 --- 16 + 9 = 25<BR>\n" );
document.write( "6 --- 25 + 11 = 36<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Each total is the square of the count number of the group<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+1%5E2 ALIGN=MIDDLE  ALT=\"1+=+1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+2%5E2 ALIGN=MIDDLE  ALT=\"4+=+2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+3%5E2 ALIGN=MIDDLE  ALT=\"9+=+3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+4%5E2 ALIGN=MIDDLE  ALT=\"16+=+4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "The question then becomes \"What group count number squared is under<BR>\n" );
document.write( "2250 when the next group count number squared goes over 2250?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%5E2 ALIGN=MIDDLE  ALT=\"50%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500 ALIGN=MIDDLE  ALT=\"2500\"   DISABLED_style= \"max-width:90%; height:auto;\" > That's too much<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%5E2 ALIGN=MIDDLE  ALT=\"48%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" > still too much<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47%5E2 ALIGN=MIDDLE  ALT=\"47%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2139 ALIGN=MIDDLE  ALT=\"2139\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "That's under <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2250 ALIGN=MIDDLE  ALT=\"2250\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2250+-+2139+=+111 ALIGN=MIDDLE  ALT=\"2250+-+2139+=+111\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=111 ALIGN=MIDDLE  ALT=\"111\"   DISABLED_style= \"max-width:90%; height:auto;\" > people of the 48th group bring the total<BR>\n" );
document.write( "up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2250 ALIGN=MIDDLE  ALT=\"2250\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, 48 groups have to arrive at school <BR>\n" );
document.write( "(There can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304+-+2139+=+165 ALIGN=MIDDLE  ALT=\"2304+-+2139+=+165\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "people in the 48th group)<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "For a formula, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the total number in the school<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the group count number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 1,2,3,4.. etc. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%5E2+%3C+T ALIGN=MIDDLE  ALT=\"g%5E2+%3C+T\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g+%2B+1%29%5E2+%3E+T ALIGN=MIDDLE  ALT=\"%28g+%2B+1%29%5E2+%3E+T\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The number of groups will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g+%2B+1 ALIGN=MIDDLE  ALT=\"g+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the<BR>\n" );
document.write( "last group having <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+-+g%5E2 ALIGN=MIDDLE  ALT=\"T+-+g%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > people <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );