document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320796>Question 320796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Before she took her last exam, the average of Tara’s exam scores was 89.  She figures that if she scores 97 on the last exam, her average for all the exams will be 90.  If she scores a 73, her average for all the exams will be 87.  How many exams, including the last one, are given in the class?  <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 #229692 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=229692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "This is a problem where you have an embarrassment of riches as far as given information goes.  Actually it is sufficient to know that the current average is 89 and a 97 on the last exam will result in an overall average of 90 to answer the question \"How many exams...?\"\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> represent the total number of exams, including the last one.  That means that up until now, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ -\ 1\"> exams have been given.  Hence, if the average for the exams already given is 89, then the sum of the scores of the exams already given must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 89(n\ -\ 1)\">.\r<BR>\n" );
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document.write( "The average of all the exams is then the sum of the first <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ -\ 1\"> exams plus 97 all divided by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> and that is equal to 90.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{89(n\ -\ 1)\ +\ 97}{n}\ =\ 90\">\r<BR>\n" );
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document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 89(n\ -\ 1)\ +\ 97\ =\ 90n\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 89n\ -\ 89\ +\ 97\ =\ 90n\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ 8\">\r<BR>\n" );
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document.write( "Therefore 8 total exams.\r<BR>\n" );
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document.write( "Check.\r<BR>\n" );
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document.write( "Seven times 89 is 623.  623 plus 97 is 720.  720 divided by 8 is 90.\r<BR>\n" );
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document.write( "Further check.\r<BR>\n" );
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document.write( "Seven times 89 is 623.  623 plus 73 is 696.  696 divided by 8 is 87.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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