document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998986>Question 998986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student missed 4 problems on a History test and received a grade of 85%. If all the problems were of equal value, how many problems were 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 #616715 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of problems on the test.<BR>\n" );
document.write( "then x-4 = number of problems you got correct.\r<BR>\n" );
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document.write( "since 85% / 100 = .85, the formula you would use is:\r<BR>\n" );
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document.write( "(x-4) / x = .85\r<BR>\n" );
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document.write( "multiply both sides of this equation by x to get:\r<BR>\n" );
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document.write( "x-4 = .85 * x\r<BR>\n" );
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document.write( "subtract .85 * x from both sides of this equation and add 4 to both sides of this equation to get:\r<BR>\n" );
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document.write( "x - .85 * x = 4\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".15 * x = 4\r<BR>\n" );
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document.write( "divide both sides of this equation by .15 to get:\r<BR>\n" );
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document.write( "x = 4 / .15\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "x = 26.66667\r<BR>\n" );
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document.write( "since x has to be an integer, and 26.66667 rounds to 27, then you would choose 27 as your answer.\r<BR>\n" );
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document.write( "when x = 27, 27-4 = 23, and 23/27 = .8518.\r<BR>\n" );
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document.write( "multiply that by 100 to get 85.18% and round to the nearest percent to get 85%.\r<BR>\n" );
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document.write( "note that the answer could also have been 26, but since 27 is closer to 26.66667, you would choose 27.\r<BR>\n" );
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document.write( "if x = 26, then x-4 = 22, and 22/26 = .8462.\r<BR>\n" );
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document.write( "multiply that by 100 to get 84.62% and round to the nearest percent to get 85%.\r<BR>\n" );
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document.write( "both 26 and 27 round to 85%, but 27 is closer, so you would choose 27.\r<BR>\n" );
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document.write( "the assumed requirements of the problem are that the number of problems has to be an integer.\r<BR>\n" );
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document.write( "there is no such requirement for the grade, so the only requirement for the grade is that it rounds to 85%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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