document.write( "Question 482207: A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results are below. How many are not using any of the three?\r
\n" ); document.write( "\n" ); document.write( "36 said they drove alone.
\n" ); document.write( "30 rode in a carpool.
\n" ); document.write( "32 rode public transportation.
\n" ); document.write( "6 used both carpool and public transportation.
\n" ); document.write( "4 used both a carpool and sometimes their own cars.
\n" ); document.write( "8 used buses as well as their own cars.
\n" ); document.write( "3 used all three methods.\r
\n" ); document.write( "\n" ); document.write( "I don't have a clue as to how to solve this. Please help!! \n" ); document.write( "
Algebra.Com's Answer #330193 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let D = the set of those who drove alone.\r\n" );
document.write( "Let C = the set of those who rode in a carpool.\r\n" );
document.write( "Let P = the set of those who rode public transportation.\r\n" );
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document.write( "There are 8 regions (subsets) which I have labeled with small\r\n" );
document.write( "letters s thru z:\r\n" );
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document.write( "The most inclusive clue we have is this one:\r\n" );
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\n" ); document.write( "3 used all three methods
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document.write( "Those 3 are in all three circles, and the only\r\n" );
document.write( "region that is common to all three circles is\r\n" );
document.write( "the middle region w, so we put 3 for w\r\n" );
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document.write( "Now we look at this:\r\n" );
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\n" ); document.write( "6 used both carpool and public transportation.
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document.write( "3 of those 6 are already accounted for in the middle region,\r\n" );
document.write( "so that leaves 6-3 or 3 to go in the other region common\r\n" );
document.write( "to circles C and P, which is region x, so we put 3 in that region:\r\n" );
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document.write( "Now we look at this:\r\n" );
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\n" ); document.write( "4 used both a carpool (C) and sometimes their own cars (D).
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document.write( "3 of those 4 are already accounted for in the middle region,\r\n" );
document.write( "so that leaves 4-3 or 1 to go in the other region common\r\n" );
document.write( "to circles C and D, which is region t, so we put 1 in that region:\r\n" );
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document.write( "Now we look at this:\r\n" );
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\n" ); document.write( "30 rode in a carpool.
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document.write( "We have numbers in 3 of the regions of circle C, so \r\n" );
document.write( "1+3+3 or 7 of those 30 are already accounted\r\n" );
document.write( "for so that leaves 30-7 or 23 to go in the remaining\r\n" );
document.write( "region of circle C, region u, so we put 23 in that region:\r\n" );
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document.write( "Now we have completed all four regions of circle C,\r\n" );
document.write( "and see that if we add up all four regions we have\r\n" );
document.write( "1+3+3+23 we have 30 in circle C, those who rode in\r\n" );
document.write( "a carpool.\r\n" );
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document.write( "Now we look at this:\r\n" );
document.write( "

\n" ); document.write( "8 used buses (public transportation) as well as their own cars (drove).
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document.write( "3 of those 8 are already accounted for in the middle region,\r\n" );
document.write( "so that leaves 8-3 or 5 to go in the other region common\r\n" );
document.write( "to circles P and D, which is region v, so we put 5 in that region:\r\n" );
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document.write( "Now we look at this:\r\n" );
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\n" ); document.write( "36 said they drove alone.
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document.write( "We have numbers in 3 of the regions of circle D, so \r\n" );
document.write( "1+3+5 or 9 of those 36 are already accounted\r\n" );
document.write( "for so that leaves 36-9 or 27 to go in the remaining\r\n" );
document.write( "region of circle D, region s, so we put 27 in that region:\r\n" );
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document.write( "Now we have completed all four regions of circle D,\r\n" );
document.write( "and see that if we add up all four regions we have\r\n" );
document.write( "27+1+3+5 we have 36 in circle C, those who drove\r\n" );
document.write( "themselves.\r\n" );
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document.write( "Now we look at this:\r\n" );
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\n" ); document.write( "32 rode public transportation.
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document.write( "We have numbers in 3 of the regions of circle P, so \r\n" );
document.write( "5+3+3 or 11 of those 32 are already accounted\r\n" );
document.write( "for so that leaves 32-11 or 21 to go in the remaining\r\n" );
document.write( "region of circle P, region y, so we put 21 in that region:\r\n" );
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document.write( "Now we know how many students are in all but one of \r\n" );
document.write( "the 8 regions, the region labeled z, that is outside\r\n" );
document.write( "all the circles.  These are what the problem asks\r\n" );
document.write( "for, how many are not using any of these.\r\n" );
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document.write( "To find this out we look at this:\r\n" );
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document.write( "Now we look at this:\r\n" );
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\n" ); document.write( "A poll was taken of 100 students
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document.write( "We have accounted for 27+1+23+5+3+3+21 or 83 of the\r\n" );
document.write( "100 students who use one or more of the three kind of \r\n" );
document.write( "transportation mentioned. The others are outside \r\n" );
document.write( "all the circles, in region z.  So the number in\r\n" );
document.write( "the region outside the circles, region z is \r\n" );
document.write( "100-83 or 17.  \r\n" );
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document.write( "So the answer is 17.\r\n" );
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document.write( "Edwin

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