document.write( "Question 820663: When the Montesano family members discussed where their annual reunion should take place, they found that of all the family members.
\n" ); document.write( " 8 would not go to the park.
\n" ); document.write( " 7 would not go to the beach.
\n" ); document.write( " 11 would not go to the family cottages.
\n" ); document.write( " 3 would go to neither a park or beach.
\n" ); document.write( " 4 would go to neither a beach nor the family cottage.
\n" ); document.write( " 6 would go to neither a park nor the family cottage.
\n" ); document.write( " 2 would not go to the park or a beach or a family cottage.
\n" ); document.write( " 1 would go to all three places.\r
\n" ); document.write( "\n" ); document.write( " What is the total of family members?\r
\n" ); document.write( "\n" ); document.write( "Please help and Thank you! \n" ); document.write( "
Algebra.Com's Answer #493686 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Here are the clues:\r\n" );
document.write( "\r\n" );
document.write( "Clues\r\n" );
document.write( "A.  8 would not go to the park.\r\n" );
document.write( "B.  7 would not go to the beach.\r\n" );
document.write( "C. 11 would not go to the family cottages.\r\n" );
document.write( "D.  3 would go to neither a park or beach.\r\n" );
document.write( "E.  4 would go to neither a beach nor the family cottage.\r\n" );
document.write( "F.  6 would go to neither a park nor the family cottage.\r\n" );
document.write( "G.  2 would not go to the park or a beach or a family cottage.\r\n" );
document.write( "H.  1 would go to all three places. \r\n" );
document.write( "\r\n" );
document.write( "Let's re-word all the clues and consider the members as\r\n" );
document.write( "non-park goers, non-beach goers, and non-cottage goers:\r\n" );
document.write( "\r\n" );
document.write( "Clues\r\n" );
document.write( "A. There are 8 non-park goers.\r\n" );
document.write( "B. There are 7 non-beach goers.\r\n" );
document.write( "C. There are 11 non-cottages goers.\r\n" );
document.write( "D. There are 3 non-park and non-beach goers.\r\n" );
document.write( "E. There are 4 non-beach and non-cottage goers.\r\n" );
document.write( "F. There ate 6 non-park and non-cottage goers.\r\n" );
document.write( "G. There are 2 non-park, non-beach and non-cottage goers.\r\n" );
document.write( "H. There is 1 who is neither a non-park, non-beach, or non-cottage goer. \r\n" );
document.write( "\r\n" );
document.write( "So lets make a three-set Venn Diagram with three mutually overlapping\r\n" );
document.write( "circles.  \r\n" );
document.write( "All the non-park goers are in the NP circle.\r\n" );
document.write( "All the non-beach goers are within in the NB circle. \r\n" );
document.write( "All the non-cottage goers are within in the NC circle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Each little letter s through z represents the \r\n" );
document.write( "number of members in the category or categories\r\n" );
document.write( "NP, NB, and/or NC the region that letter is in:\r\n" );
document.write( "\r\n" );
document.write( "s = the number of NP only\r\n" );
document.write( "t = the number of NP and NB, but not NC\r\n" );
document.write( "u = the number of NB only\r\n" );
document.write( "v = the number of NP and NC but not NB\r\n" );
document.write( "w = the number of NP,NB, and NC \r\n" );
document.write( "x = the number of NB,NC, but not NP\r\n" );
document.write( "y = the number of NC only\r\n" );
document.write( "z = the number of not NP, not NB, and not NC\r\n" );
document.write( "\r\n" );
document.write( "So now we can look at the clues and determine:\r\n" );
document.write( "\r\n" );
document.write( "Clues\r\n" );
document.write( "A. There are 8 non-park goers. So s+t+v+w=8\r\n" );
document.write( "B. There are 7 non-beach goers. So t+u+w+x=7\r\n" );
document.write( "C. There are 11 non-cottages goers. So v+w+x+y=11\r\n" );
document.write( "D. There are 3 non-park and non-beach goers. So t+w=3\r\n" );
document.write( "E. There are 4 non-beach and non-cottage goers. So w+x=4\r\n" );
document.write( "F. There ate 6 non-park and non-cottage goers. So v+w=6\r\n" );
document.write( "G. There are 2 non-park, non-beach and non-cottage goers. So w=2\r\n" );
document.write( "H. There is 1 who is neither a non-park, non-beach, or non-cottage goer. So z=1  \r\n" );
document.write( "\r\n" );
document.write( "From G we have w=2\r\n" );
document.write( "From H we have z=1\r\n" );
document.write( "From D we have t+w=3 and since w=2, t+2=3 and so t=1\r\n" );
document.write( "From E we have w+x=4 and since w=2, 2+x=4 and so x=2\r\n" );
document.write( "From F we have v+w=6 and since w=2, v+2=6 and so v=4\r\n" );
document.write( "From A we have s+t+u+v=8, so s+1+4+2=8, so s=1\r\n" );
document.write( "From B we have t+u+w+x=7, so 1+u+2+2=7, so u=2\r\n" );
document.write( "From C we have v+w+x+y=11, so 4+2+2+y=11, so y=3 \r\n" );
document.write( "\r\n" );
document.write( "So we have a total of s+t+u+v+w+x+y+z = 1+1+2+4+2+2+3+1 = 16\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer: 16 Montesano family members.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );