document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=587818>Question 587818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student completes three assessment tasks and receives marks of 25, 15 and 12. She completes a fourth assessment task and achieves an overall average (mean) of 14.5 for the four tests?<BR>\n" );
document.write( "a) Assuming that x is the result she obtained on the fourth assessment task, write the information given as an algebraic equation.<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 #374270 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=374270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The total of her four scores is the sum of the three known scores (25 + 15 + 12) plus x, her unknown score on the fourth assessment task. If you divide that total by 4 (which is the number of scores) you will get the average score on the four assessment tasks. The problem tells you that the average score is 14.5<BR>\n" );
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document.write( "So let's set this up as an equation. Begin by writing the sum of the four scores:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2B+15+%2B+12+%2B+x ALIGN=MIDDLE  ALT=\"25+%2B+15+%2B+12+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide that sum by 4 to find the average:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825+%2B+15+%2B+12+%2B+x%29%2F4 ALIGN=MIDDLE  ALT=\"%2825+%2B+15+%2B+12+%2B+x%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And since we know that the average is 14.5 we can set this equal to 14.5:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825+%2B+15+%2B+12+%2B+x%29%2F4+=+14.5 ALIGN=MIDDLE  ALT=\"%2825+%2B+15+%2B+12+%2B+x%29%2F4+=+14.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can solve this for x. Begin by adding the first three scores of 25, 15, and 12 to get a total of 52. This makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2852+%2B+x%29%2F4+=+14.5 ALIGN=MIDDLE  ALT=\"%2852+%2B+x%29%2F4+=+14.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then we can get rid of the denominator 4 on the left side by multiplying both sides of the equation by 4 as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2A%2852+%2B+x%29%29%2F4+=+4%2A14.5 ALIGN=MIDDLE  ALT=\"%284%2A%2852+%2B+x%29%29%2F4+=+4%2A14.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side, the 4 in the numerator cancels with the 4 in the denominator, and on the right side the product of 4 times 14.5 is 58. This reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52+%2B+x+=+58 ALIGN=MIDDLE  ALT=\"52+%2B+x+=+58\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next you can get rid of the 52 on the left side by subtracting 52 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer to this problem. She scored 6 on the fourth assessment task.<BR>\n" );
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document.write( "So, if she scored a 6 on the fourth assessment task, the resulting average should be 14.5.<BR>\n" );
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document.write( "Let's check that. By scoring an 6 on the final assessment task, the four scores become 25 + 15 + 12 + 6. Add these 4 scores and the total is 58. Then find the mean by dividing the total 58 points by 4 and the answer is 14.5, so the answer checks.<BR>\n" );
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document.write( "Hope this helps you to understand the problem (and also see that she didn't prepare enough so that she did well on the fourth assessment task).<BR>\n" );
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