document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=788871>Question 788871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sue is packing boxes ,she packed 55 boxes in 5 hours. Since she is getting better at it, each hour she packs 2 more than the previous hour. How many boxes did she pack in the fourth hour?<BR>\n" );
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document.write( "One stumped nana trying to help grandson<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 #478669 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=478669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE STORY:<BR>\n" );
document.write( "I read the problem as meaning that Sue packed a total of 55 boxes during hours 1 through 5, and the question is how many boxes did Sue pack in the fourth of those 5 hours.<BR>\n" );
document.write( "In those 5 hours Sue has been packing boxes at an average speed of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2F5=11 ALIGN=MIDDLE  ALT=\"55%2F5=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > boxes per hour.<BR>\n" );
document.write( "Since her packing speed increases at a constant rate, her average rate for the 5 hours is the same as her rate for the third hour (the one in the middle of the 5).<BR>\n" );
document.write( "So, during the third hour she packed 11 boxes.<BR>\n" );
document.write( "The 2 extra boxes packed in the fourth hour (for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2B2=highlight%2813%29 ALIGN=MIDDLE  ALT=\"11%2B2=highlight%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > boxes) compensate for the fact that during the second hour Sue she had packed 2 boxes less than 11.<BR>\n" );
document.write( "Also, compared to the third hour, the 4 extra boxes packed during the fifth hour compensate for the 4 fewer boxes packed during the first hour.<BR>\n" );
document.write( "So, Sue packed 7 boxes, the first hour, 9 the second hour, 11 the third hour, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2813%29 ALIGN=MIDDLE  ALT=\"highlight%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the fourth hour, and 15 the fifth hour.<BR>\n" );
document.write( "It all adds up.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B9%2B11%2B13%2B15=55 ALIGN=MIDDLE  ALT=\"7%2B9%2B11%2B13%2B15=55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "HOW TO SHOW THE WORK:<BR>\n" );
document.write( "If only the final result is required, we are done.<BR>\n" );
document.write( "If this is an elementary, or middle school problem, probably they expect the student to use \"guess and check\", taking a guess on how many boxes were packed the first hour, and working from there to find a 5-hour total. If the total is not right, you have to make a new guess and calculate a new total. If the total is too low, the first hour guess has to be increased; if the total is too high, the first hour guess has to be decreased. A table can be made showing the guesses and the results. When you guess that 7 boxes were packed the first hour , you get a 5-hour total of 55 boxes, and a fourth hour count of 13 boxes (the answer to the problem).<BR>\n" );
document.write( "If this is an advanced high school math problem, and the student is studying arithmetic sequences (also called arithmetic progressions in some places), the teacher probably expects to see a bunch of formulas.<BR>\n" );
document.write( "The arithmetic sequence terms would be given by<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= first term = numbers of boxes packed thr first hour<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= common difference = difference in the numbers of boxes packed from one hour to the next.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= boxes backed the nth hour<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=a%5B1%5D%2A%281%2B%28n-1%29d%29%2An%2F2 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=a%5B1%5D%2A%281%2B%28n-1%29d%29%2An%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= sum of the first n terms = total number of boxes packed in n hours.<BR>\n" );
document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2 ALIGN=MIDDLE  ALT=\"d=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B5%5D=55 ALIGN=MIDDLE  ALT=\"S%5B5%5D=55\"   DISABLED_style= \"max-width:90%; height:auto;\" >and we have to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55=%282%2Aa%5B1%5D%2B%285-1%29%2A2%29%2A5%2F2 ALIGN=MIDDLE  ALT=\"55=%282%2Aa%5B1%5D%2B%285-1%29%2A2%29%2A5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55=%282%2Aa%5B1%5D%2B4%2A2%29%2A5%2F2 ALIGN=MIDDLE  ALT=\"55=%282%2Aa%5B1%5D%2B4%2A2%29%2A5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55=%282a%5B1%5D%2B8%29%2A5%2F2 ALIGN=MIDDLE  ALT=\"55=%282a%5B1%5D%2B8%29%2A5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55=%2810a%5B1%5D%2B40%29%2F2 ALIGN=MIDDLE  ALT=\"55=%2810a%5B1%5D%2B40%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A55=10a%5B1%5D%2B40 ALIGN=MIDDLE  ALT=\"2%2A55=10a%5B1%5D%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110=10a%5B1%5D%2B40 ALIGN=MIDDLE  ALT=\"110=10a%5B1%5D%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110-40=10a%5B1%5D ALIGN=MIDDLE  ALT=\"110-40=10a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70=10a%5B1%5D ALIGN=MIDDLE  ALT=\"70=10a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F10=a%5B1%5D ALIGN=MIDDLE  ALT=\"70%2F10=a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=7 ALIGN=MIDDLE  ALT=\"a%5B1%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, we plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=4 ALIGN=MIDDLE  ALT=\"n=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=7 ALIGN=MIDDLE  ALT=\"a%5B1%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2 ALIGN=MIDDLE  ALT=\"d=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the number of boxes packed the fourth hour.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=7%2B%284-1%29%2A2 ALIGN=MIDDLE  ALT=\"a%5B4%5D=7%2B%284-1%29%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=7%2B3%2A2 ALIGN=MIDDLE  ALT=\"a%5B4%5D=7%2B3%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=7%2B6 ALIGN=MIDDLE  ALT=\"a%5B4%5D=7%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=highlight%2813%29 ALIGN=MIDDLE  ALT=\"a%5B4%5D=highlight%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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