document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134236>Question 1134236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! Looking at my teachers notes, they do not make sense. I am also waiting on an emai from her for extra help, but I figure ask here as well since I’ve gotten help before and it does help reading this and asking my teacher. The question is:\r<BR>\n" );
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document.write( "A class of 28 students took a 100 point test. If the mean was 68, is it possible that 23 of the students got a score of 63 or lower?\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751554 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Yes it is possible, and here's why:\r<BR>\n" );
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document.write( "Focus on the phrase \" 23 of the students got a score of 63 or lower\". Let's assume that all 23 students got the same score of 63, which is the highest possible for this group. This would mean that the total sum of the scores so far is 23*63 = 1449. Basically if you had 23 copies of \"63\" added up, you'd get to 1449.\r<BR>\n" );
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document.write( "Add on 5*x which represents the idea of having 5 other students score some other value x. Keep in mind that x is in the interval from 0 to 100. Anything outside this interval does not make sense. You can't get a negative score. You cannot get a score over 100 (assume there's no extra credit)\r<BR>\n" );
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document.write( "So we add 5x to 1449 to get 5x+1449. This total sum is divided over the number of students, which is 28, to get this expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B1449%29%2F28 ALIGN=MIDDLE  ALT=\"%285x%2B1449%29%2F28\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This expression represents the average of all 28 students. The first 23 scored a 63, while the other 5 got a score of 'x' (to be determined)\r<BR>\n" );
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document.write( "Set this expression equal to the target average we want, which is 68. Let's solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B1449%29%2F28+=+68 ALIGN=MIDDLE  ALT=\"%285x%2B1449%29%2F28+=+68\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B1449+=+28%2A68 ALIGN=MIDDLE  ALT=\"5x%2B1449+=+28%2A68\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 28\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B1449+=+1904 ALIGN=MIDDLE  ALT=\"5x%2B1449+=+1904\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B1449-1449+=+1904-1449 ALIGN=MIDDLE  ALT=\"5x%2B1449-1449+=+1904-1449\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1449 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+455 ALIGN=MIDDLE  ALT=\"5x+=+455\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2F5+=+455%2F5 ALIGN=MIDDLE  ALT=\"5x%2F5+=+455%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+91 ALIGN=MIDDLE  ALT=\"x+=+91\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the other five students must score 91 on each test so that the entire class averages a 68.\r<BR>\n" );
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document.write( "So it is possible, and I'm sure there are other scenarios where you can have the class average a 68 even if you don't have two groups scoring the same. Though of course, if the first group has too low of scores then at some point the other group won't have enough to bring up the overall average. <BR>\n" );
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