document.write( "Question 809820: At a certain summer camp the participants were polled to find out what type of
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Algebra.Com's Answer #487853 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since it makes things easier to use the first letter of what\r\n" );
document.write( "each set is composed of, and since Documents and Dramas both \r\n" );
document.write( "start with D, I changed Dramas to Musicals.  That way we can\r\n" );
document.write( "use set D for documentaries, C for comedies, and M for musicals,\r\n" );
document.write( "with no conflicts of letters.\r\n" );
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document.write( "                   CLUES  \r\n" );
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document.write( "1.  160 liked Comedies.                 (1 set is mentioned)\r\n" );
document.write( "2.  160 liked to watch Documentaries,   (1 set mentioned)\r\n" );
document.write( "3   190 liked to watch Musicals,        (1 set mentioned)\r\n" );
document.write( "4.  20 campers like all three programs, (3 sets mentioned)\r\n" );
document.write( "5.  50 watched Comedies and Documentaries, but not Musicals,  (3 sets mentioned) \r\n" );
document.write( "6.  70 liked to watch Documentaries and Musical, but not Comedies. (3 sets mentioned)  \r\n" );
document.write( "7.  130 watched Musicals, but not Comedies. (2 sets mentioned) \r\n" );
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document.write( "The little letters will represent how many are\r\n" );
document.write( "in each of the 8 regions.\r\n" );
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document.write( "Region                 They\r\n" );
document.write( "with       watch      do not\r\n" );
document.write( "this       these      watch\r\n" );
document.write( "many     programs     these \r\n" );
document.write( "campers              programs\r\n" );
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document.write( "  a         C           D, M\r\n" );
document.write( "  b        C,D            M\r\n" );
document.write( "  e         D            C,M\r\n" );
document.write( "  f        C,M            D\r\n" );
document.write( "  g       C,D,M         ----\r\n" );
document.write( "  h        D,M            C\r\n" );
document.write( "  i         M            C,D\r\n" );
document.write( "  j       ----          C,D,M   \r\n" );
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document.write( "Since all participated in the survey, and none \r\n" );
document.write( "did not like to watch any of the three kinds of \r\n" );
document.write( "programs, so we know that j=0.\r\n" );
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document.write( "We begin with the clues that mention the most \r\n" );
document.write( "number of sets.\r\n" );
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document.write( "Clue 4 tells us that g=20. \r\n" );
document.write( "Clue 5 tells us that b=50.\r\n" );
document.write( "Clue 6 tells us that h=70.    \r\n" );
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document.write( "Now we can find e from clue 2\r\n" );
document.write( "b+g+h+e = 120 and b+g+h=50+20+70=140,\r\n" );
document.write( "so e=140-120=20.\r\n" );
document.write( "We can find i from clue 7.\r\n" );
document.write( "h+i = 130, and since h=70, i=130-70=60,\r\n" );
document.write( "so now we have\r\n" );
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document.write( "Now we can find f from clue 3.\r\n" );
document.write( "f+g+h+i=190, and g+h+i=20+70+60=150,\r\n" );
document.write( "so f = 190-150=40.  So we have\r\n" );
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document.write( "Finally we can find a from clue 1.\r\n" );
document.write( "a+b+f+g=160, and b+f+g=50+40+20=110\r\n" );
document.write( "so a=160-110=50.  So now our Venn\r\n" );
document.write( "diagram is complete:\r\n" );
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document.write( "Now to find the total number of campers we add\r\n" );
document.write( "a+b+e+f+g+h+i+j = \r\n" );
document.write( "50+50+20+40+20+70+60+0 = 310 campers.\r\n" );
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document.write( "Edwin
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