document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516011>Question 516011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a student missed 6 questions and received 87% if all the problems where equal value how many problems where on the test </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344406 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=344406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The exam has an unknown number of questions. Let's call that number x.<BR>\n" );
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document.write( "The student misses 6 questions. That means that the number of questions that the student got correct was x - 6. If you divide the number that the student answered correctly by the total number of questions, you should get the score of 87% or 0.87.<BR>\n" );
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document.write( "In equation form, the numerator is the number correctly answered (x - 6) and the denominator is the total number of questions (x) and that division should result in an answer of 0.87. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%2Fx+=+0.87 ALIGN=MIDDLE  ALT=\"%28x-6%29%2Fx+=+0.87\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To get rid of the denominator, multiply both sides of the equation by x. On the left side, the x multiplier cancels with the x denominator, and the left side becomes just the numerator of x - 6. On the right side the multiplication results in the product of 0.87 times x. Therefore, the after multiplying both sides of the equation by x and simplifying the equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+6+=+0.87x ALIGN=MIDDLE  ALT=\"x+-+6+=+0.87x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel the minus 6 on the left side by adding +6 to both sides. The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.87x+%2B+6 ALIGN=MIDDLE  ALT=\"x+=+0.87x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 0.87x from both sides. On the left side, taking 0.87x from x results in 0.13x. On the right side, this subtraction cancels the 0.87x. The equation has now become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.13x+=+6 ALIGN=MIDDLE  ALT=\"0.13x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x by dividing both sides by 0.13 and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6%2F0.13 ALIGN=MIDDLE  ALT=\"x+=+6%2F0.13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The division on the right side results in 46.1538<BR>\n" );
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document.write( "Since the decimal part of this answer (that is, the 0.1538) doesn't make sense (what does 0.1538 of a question mean?) just round off the answer to 46 questions.<BR>\n" );
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document.write( "That means that by missing 6 questions, the student got 40 of 46 correct. If you divide 40 by 46 you would find that the student got a score of 86.956% which the teacher rounded to 87%. That checks our answer.<BR>\n" );
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document.write( "The answer to this problem is that the exam had a total of 46 questions.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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