document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205948>Question 1205948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To earn an A in a​ course, a boy must have a final average of at least 84​%. On the first four​ examinations, he has grades of 79​%, 85​%, 75​%, and 75​%. If the final examination counts as two ​grades, what must he get on the final to earn an A in 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 #843064 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The correction from the second tutor is not right.  The grade on the final exam counts as much as two of the other grades, so in effect 6 grades are being averaged.<br><BR>\n" );
document.write( "Here is an alternative method for solving a problem like this involving the average of numbers that are close together.<br><BR>\n" );
document.write( "Consider how much each of the existing grades is above or below the desired average:<br><BR>\n" );
document.write( "79: -5<BR>\n" );
document.write( "85: +1<BR>\n" );
document.write( "75: -9<BR>\n" );
document.write( "75: -9<br><BR>\n" );
document.write( "Together, the four grades are -22 compared to the desired average.  To achieve the desired average, the final exam must be +22 compared to the desired average.<br><BR>\n" );
document.write( "Since the final exam counts twice as much as each of the others, the grade on the final exam must be 22/2 = 11 over the desired average.<br><BR>\n" );
document.write( "ANSWER: The minimum grade needed to achieve an average of at least 84% is 84+11 = 95%.<br><BR>\n" );
document.write( "CHECK: 79+85+75+75+95+95 = 504; 504/6 = 84<br><BR>\n" );
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