document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194368>Question 1194368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Student A, Student B, and Student C have been hired to help scientists develop a new flavour of juice. There are 4200 samples to test. Each sample either contains<BR>\n" );
document.write( "blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90% of the samples containing blueberry and reports correctly on exactly 88% of the samples that do not contain blueberry. The results for all three students are shown below.<BR>\n" );
document.write( "                                Student A           Student B       Student C<BR>\n" );
document.write( "%samples containing blueberry     90%                 98%             (2m)%<BR>\n" );
document.write( "%samples not containing blueberry 88%                 86%             (4m)%\r<BR>\n" );
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document.write( "Student B reports 315 more samples as containing blueberry than Student A. For<BR>\n" );
document.write( "some positive integers m, the total number of samples that the three students report as containing blueberry is equal to a multiple of 5 between 8000 and 9000. What is the sum of all such values of m.\r<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 #848462 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's break down the problem and find the sum of all possible values of 'm'.\r<BR>\n" );
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document.write( "**1. Define Variables:**\r<BR>\n" );
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document.write( "* Let 'x' be the number of samples containing blueberries.<BR>\n" );
document.write( "* Let 'y' be the number of samples not containing blueberries. \r<BR>\n" );
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document.write( "**2. Set up Equations**\r<BR>\n" );
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document.write( "* **Total Samples:** x + y = 4200 <BR>\n" );
document.write( "* **Student B Reports More Blueberries:** <BR>\n" );
document.write( "    * 0.98x - 0.90x = 315 <BR>\n" );
document.write( "    * 0.08x = 315<BR>\n" );
document.write( "    * x = 3937.5\r<BR>\n" );
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document.write( "* **Since the number of samples must be whole numbers:**<BR>\n" );
document.write( "    * x = 3938 <BR>\n" );
document.write( "    * y = 4200 - 3938 = 262\r<BR>\n" );
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document.write( "**3. Determine the Number of Samples Reported as Containing Blueberries by Each Student:**\r<BR>\n" );
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document.write( "* **Student A:** 0.90x = 0.90 * 3938 = 3544.2 ≈ 3544 <BR>\n" );
document.write( "* **Student B:** 0.98x = 0.98 * 3938 = 3861.24 ≈ 3861<BR>\n" );
document.write( "* **Student C:** (2m/100) * x = (2m/100) * 3938 = 78.76m ≈ 78.76m\r<BR>\n" );
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document.write( "**4. Find the Total Number of Samples Reported as Containing Blueberries by All Students:**\r<BR>\n" );
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document.write( "* Total = Student A + Student B + Student C<BR>\n" );
document.write( "* Total = 3544 + 3861 + 78.76m <BR>\n" );
document.write( "* Total = 7405 + 78.76m\r<BR>\n" );
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document.write( "**5. Determine the Range for Total Samples Containing Blueberries**\r<BR>\n" );
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document.write( "* The total number of samples reported as containing blueberries is a multiple of 5 between 8000 and 9000.<BR>\n" );
document.write( "* Therefore: <BR>\n" );
document.write( "    * 8000 ≤ 7405 + 78.76m ≤ 9000<BR>\n" );
document.write( "    * 595 ≤ 78.76m ≤ 1595\r<BR>\n" );
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document.write( "**6. Find Possible Values of 'm'**\r<BR>\n" );
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document.write( "* 595 / 78.76 ≤ m ≤ 1595 / 78.76<BR>\n" );
document.write( "* 7.55 ≤ m ≤ 20.23\r<BR>\n" );
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document.write( "* Since 'm' is a positive integer:<BR>\n" );
document.write( "    * Possible values of 'm': 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\r<BR>\n" );
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document.write( "**7. Calculate the Sum of All Possible Values of 'm'**\r<BR>\n" );
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document.write( "* Sum = 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 <BR>\n" );
document.write( "* Sum = 153\r<BR>\n" );
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document.write( "**Therefore, the sum of all possible values of 'm' is 153.**<BR>\n" );
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