document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196293>Question 1196293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Allanʹs 4 quiz scores in his math class are 87, 89, 88, and 78. What score does he need to obtain on<BR>\n" );
document.write( "his exam to average an 85 if an exam counts as much as two quizzes? </SPAN>\n" );
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document.write( "x = score on the exam<BR>\n" );
document.write( "2x = equivalent score on a quiz (since the exam counts for two quizzes)<BR>\n" );
document.write( "For instance if you got an 82 on the exam, then it is equivalent to 2*82 = 164 points for a quiz. <BR>\n" );
document.write( "It might be helpful to think of it like getting 82's on two different extra quizzes.\r<BR>\n" );
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document.write( "It also might be helpful to think of the 2x as x+x<BR>\n" );
document.write( "So that we can break things further down\r<BR>\n" );
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document.write( "A = set of scores<BR>\n" );
document.write( "A = {87, 89, 88, 78, x, x}<BR>\n" );
document.write( "Note I listed x twice<BR>\n" );
document.write( "There are 6 elements in set A\r<BR>\n" );
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document.write( "Now compute the average. Do so by adding up the scores and dividing by the number of scores (6)<BR>\n" );
document.write( "So we get:<BR>\n" );
document.write( "(87+89+88+78+x+x)/6<BR>\n" );
document.write( "which simplifies to <BR>\n" );
document.write( "(342+2x)/6\r<BR>\n" );
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document.write( "Set this average equal to the target 85 and solve for x.<BR>\n" );
document.write( "(342+2x)/6 = 85<BR>\n" );
document.write( "342+2x = 6*85<BR>\n" );
document.write( "342+2x = 510<BR>\n" );
document.write( "2x = 510-342<BR>\n" );
document.write( "2x = 168<BR>\n" );
document.write( "x = 168/2<BR>\n" );
document.write( "x = 84\r<BR>\n" );
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document.write( "Answer: <font color=red>84</font><BR>\n" );
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