document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662795>Question 662795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An average score of 80 to 90 in a math class receives a B grade. A student has scores of 92, 66, 72 and 88 of four tests. Find the range of scores on the fifth test that will give the student a B for the course.<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 #412544 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=412544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I interpret the wording as meaning that 80 and 90 are both a B.<BR>\n" );
document.write( "I'll solve based on that.<BR>\n" );
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document.write( "WITH ROUNDING:<BR>\n" );
document.write( "If we are going to be realistic, we have to consider rounding.<BR>\n" );
document.write( "I expect that an average of 79.5 would be rounded up to 80, and would be enough for a B.<BR>\n" );
document.write( "I expect that an average of 90.5 would be rounded up to 91, and that would be enough for an A,<BR>\n" );
document.write( "but any average of less than 90.5 (even a 90.4) would be a B.<BR>\n" );
document.write( "So I am starting from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79.5%3C=average%3C90.5 ALIGN=MIDDLE  ALT=\"79.5%3C=average%3C90.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I am assuming they calculate the average as the sum of all tests grades divided by the number of tests.<BR>\n" );
document.write( "If the score in the last test is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the average will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=average=%2892%2B66%2B72%2B88%2Bx%29%2F5=%28318%2Bx%29%2F5 ALIGN=MIDDLE  ALT=\"average=%2892%2B66%2B72%2B88%2Bx%29%2F5=%28318%2Bx%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now my equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79.5%3C=%28318%2Bx%29%2F5%3C90.5 ALIGN=MIDDLE  ALT=\"79.5%3C=%28318%2Bx%29%2F5%3C90.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying all sides of the signs times 5, we get an equivalent inequality<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79.5%2A5%3C=318%2Bx%3C90.5%2A5 ALIGN=MIDDLE  ALT=\"79.5%2A5%3C=318%2Bx%3C90.5%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=397.5%3C=318%2Bx%3C452.5 ALIGN=MIDDLE  ALT=\"397.5%3C=318%2Bx%3C452.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=318 ALIGN=MIDDLE  ALT=\"318\"   DISABLED_style= \"max-width:90%; height:auto;\" > from all sides of the signs, we an the equivalent inequality<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=397.5%3C=318%2Bx%3C452.5 ALIGN=MIDDLE  ALT=\"397.5%3C=318%2Bx%3C452.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=397.5-318%3C=318%2Bx-318%3C452.5-318 ALIGN=MIDDLE  ALT=\"397.5-318%3C=318%2Bx-318%3C452.5-318\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79.5%3C=x%3C132 ALIGN=MIDDLE  ALT=\"79.5%3C=x%3C132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So there is no possibility of getting an A, and a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2880%29 ALIGN=MIDDLE  ALT=\"highlight%2880%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the fifth test is needed to get an A as the final grade.<BR>\n" );
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document.write( "WITH ROUNDING:<BR>\n" );
document.write( "If the average has to be exactly 80.0 for a B,<BR>\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%3C=%28318%2Bx%29%2F5 ALIGN=MIDDLE  ALT=\"80%3C=%28318%2Bx%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%3C=318%2Bx ALIGN=MIDDLE  ALT=\"400%3C=318%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=82%3C=x ALIGN=MIDDLE  ALT=\"82%3C=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2882%29 ALIGN=MIDDLE  ALT=\"highlight%2882%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the fifth test is needed for a B. </SPAN>\n" );
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