document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27621>Question 27621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help answering the following math problem: Going into the final exam, which will count as two-thirds of the final grade, Mike has test scores of 86, 80, 84, and 90.  What score does Mike need on the final in order to earn a B, which requires an average score of 80?  What does he need to earn an A, which requires an average of 90?\r<BR>\n" );
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document.write( "I began answering the first part of the problem by using the following equation and solving for x: 86 + 80 + 84 + 90 + 2/3x = 340 + 2/3x.  X = 90.  So, Mike needs a score of 90 to earn a B and using the same formula, he needs a score of 165 to earn an A.  \r<BR>\n" );
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document.write( "However, I am not sure if I solved this problem correctly.  Please advise where I might have messed up.  Thank you in advance.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15046 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE MY COMMENTS BELOW.<BR>\n" );
document.write( "Going into the final exam, which will count as two-thirds of the final grade<BR>\n" );
document.write( "FIRSTLY WHAT IS MEANT BY THIS STATEMENT?IT IS NOT CLEAR..DOES IT MEAN 2/3 RD.OF MARKS GOT IN THE FINAL EXAM WILL BE COUNTED?IT DOES NOT MAKE SENSE...IF IT HAS NO RELEVANCE TO THE PROBLEM IT IS OK......<BR>\n" );
document.write( "ORELSE THE ONLY INTERPRETATION I CAN THINK OF IS THAT THE LAST EXAM IS FOR A TOTAL OF MAXIMUM 150 MARKS AND HENCE TO BRING IT DOWN TO A MAXIMUM OF 100 MARKS AVERAGE AS IS THE CASE WITH OTHER EXAM MARKS , WE NEED TO MULTIPLY THE MARKS GOT IN THE FINAL EXAM BY 2/3..<BR>\n" );
document.write( " Mike has test scores of 86, 80, 84, and 90.  What score does Mike need on the final in order to earn a B, which requires an average score of 80?<BR>\n" );
document.write( "OK WITH THIS THE PROBLEM IS COMPLETE AND CAN BE SOLVED AS SHOWN BELOW..\r<BR>\n" );
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document.write( "What does he need to earn an A, which requires an average of 90?<BR>\n" );
document.write( "THIS IS A SECOND PART OF THE PROBLEM WHICH CAN BE SOLVED IN SAME WAY..<BR>\n" );
document.write( "I began answering the first part of the problem by using the following equation and solving for x: 86 + 80 + 84 + 90 + 2/3x = 340 + 2/3x. <BR>\n" );
document.write( "THIS IS NOT THE EQN..THE EQN. IS <BR>\n" );
document.write( "340+2X/3= 5*80=400...OR 340+X=400 ,IF WE NEGLECT THAT 2/3 PART OF THE QUESTION AS I SAID ABOVE.<BR>\n" );
document.write( "SEE THE PROBLEM SOLVED BY ME EARLIER (GIVEN BELOW)TO COMPARE YOUR WORKING WITH MINE.OF COURSE AS I DEDUCED LATER YOUR WORKING MUST BE APPARENTLY SAME AND OK... .THE ANSWER IS X=60..AND IF THAT 2/3 FACTOR IS REALLY WHAT YOU MEANT THEN YOUR ANSWER OF X=90 IS CORRECT SINCE IF ONLY 2/3 OF THE SCORE IS TAKEN WE GET 90*2/3=60<BR>\n" );
document.write( " X = 90. <BR>\n" );
document.write( " So, Mike needs a score of 90 to earn a B <BR>\n" );
document.write( "CORRECT!!! IF THE ABOVE INTERPRETATION IS CORRECT..<BR>\n" );
document.write( "and using the same formula, he needs a score of 165 to earn an A.<BR>\n" );
document.write( "CORRECT!!! IF THE ABOVE INTERPRETATION IS CORRECT..  \r<BR>\n" );
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document.write( "However, I am not sure if I solved this problem correctly.<BR>\n" );
document.write( "HAVE CONFIDENCE IN YOUR ABILITY!YOU HAVE DONE EXTREMELY WELL AND BOUND TO DO BETTER WITH CONFIDENCE..<BR>\n" );
document.write( "  Please advise where I might have messed up. <BR>\n" );
document.write( "NO NO NO....A THOUSAND TIMES..YOU HAVE DONE EXCEPTIONALLY WELL..DONT FEEL THAT WAY AT ALL ...YOU ARE ON YOUR WAY TO BECOME AN EXPERT!!!<BR>\n" );
document.write( " Thank you in advance.  \r<BR>\n" );
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document.write( "SEE THE FOLLOWING EXAMPLE...<BR>\n" );
document.write( "Judy needs a mean(average) socre of 86 on four tests to earn a midterm grade of B. If the the mean of her first three test was 83, what is the lowest score ona 100-point scale that she can receive on the fourth test to have a midterm grade of B? **Let 't' represent the unknown test grade<BR>\n" );
document.write( "1 solutions\r<BR>\n" );
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document.write( "Answer 14973 by venugopalramana(912)   on 2006-02-15 23:37:26 (Show Source): \r<BR>\n" );
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document.write( "Judy needs a mean(average) socre of 86 on four tests to earn a midterm grade of B. If the the mean of her first three test was 83, what is the lowest score ona 100-point scale that she can receive on the fourth test to have a midterm grade of B? **Let 't' represent the unknown test grade<BR>\n" );
document.write( "TOTAL TESTS =4<BR>\n" );
document.write( "AVERAGE NEEDED TO GET B GRADE = 86<BR>\n" );
document.write( "SO TOTAL MARKS NEEDED IN 4 TESTS =AVERAGE *NUMBER OF TESTS=86*4=344<BR>\n" );
document.write( "NUMBER OF TESTS ATTENDED BY JUDY =3<BR>\n" );
document.write( "AVERSGE GOT IN 3 TESTS =83<BR>\n" );
document.write( "SO TOTAL MARKS GOT IN 3 TESTS =AVERAGE * NUMBER OF TESTS=83*3= 249<BR>\n" );
document.write( "SO MARKS TO BE GOT IN 4 TH. TEST =344-249= 95\r<BR>\n" );
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