document.write( "Question 1122902: A study of 115 people shows that 85 eat breakfast, 58 use dental floss
\n" ); document.write( "regularly, and 27 subscribe to the morning paper. Among those who eat
\n" ); document.write( "breakfast, 52 floss regularly and 15 get the morning paper. Further, 10
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Algebra.Com's Answer #739080 by ikleyn(52835) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "The number of those who eat breakfast, or floss regularly, or get the morning paper \r\n" );
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document.write( "    115 - 14 = 101.\r\n" );
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document.write( "Let B is the set of those who eat breakfast   (and the number of people in this set, at the same time, which is 85 - given !).\r\n" );
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document.write( "Let F is the set of those who floss regularly (and the number of people in this set, at the same time, which is 58 - given !).\r\n" );
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document.write( "Let P is the set of those who subscribe paper (and the number of people in this set, at the same time, which is 27 - given !).\r\n" );
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document.write( "Let BF is the intersection of the sets B and F (and the number of people in this intersection, at the same time, which is 52 - given !).\r\n" );
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document.write( "Let BP is the intersection of the sets B and P (and the number of people in this intersection, at the same time, which is 15 - given !).\r\n" );
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document.write( "Let BFP is the intersection of the sets B, F and P (and the number of people in this intersection, at the same time, which is 10 - given !).\r\n" );
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document.write( "The number of those who do any of these morning activities is 115 - 14 = 101.\r\n" );
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document.write( "This number, which is the number of people in the union of the sets B, F and P, can be calculated in other way, too, using the formula\r\n" );
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document.write( "   101 = n(B U F U P) = B + F + P - BF - BP - FP + BFP.    *()\r\n" );
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document.write( "In this equation, we know every term of the right side, except FP (which is under the question b) ).\r\n" );
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document.write( "So, we substitute all known values into equation (*), and we get\r\n" );
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document.write( "    101 = 85 + 58 + 27 - 52 - 15 - FP + 10.\r\n" );
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document.write( "Now we can easily find the value of FP as\r\n" );
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document.write( "    FP = 85 + 58 + 27 -52 - 15 + 10 - 101 = 12.\r\n" );
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document.write( "Answer.  The number of those who use dental floss regularly and also get the morning paper is 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding the formula (*), which is a key in the solution, see the lesson\r
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\n" ); document.write( "\n" ); document.write( "For many other similar solved problems, see the lesson\r
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