document.write( "Question 630307: Sets A, B , and C have 6 members in common. Sets A and B have a total of 17 members in common. Sets B and C have a total of 10 members in common. If each members of set B is contained in at least one of the other two sets, how many members are in set B? \n" ); document.write( "
Algebra.Com's Answer #396843 by Edwin McCravy(20060)\"\" \"About 
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document.write( "All elements within the green circle are members of A.\r\n" );
document.write( "All elements within the blue circle are members of B.\r\n" );
document.write( "All elements within the red circle are members of C.\r\n" );
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document.write( "Let t,u,v,w,x,y,z represent the number of members in each of the regions.\r\n" );
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document.write( ">>...Sets A, B , and C have 6 members in common...<<\r\n" );
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document.write( "That is the region with x in it because that is the only region\r\n" );
document.write( "that is inside all three circles, so we put x=6 there, like this:\r\n" );
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document.write( ">>...Sets A and B have a total of 17 members in common...<<\r\n" );
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document.write( "The only regions common to A and B are the ones with x elements\r\n" );
document.write( "and u elements.  Since x=6, u must be 17-6 or 11.  So we put\r\n" );
document.write( "u=11 in there, like this:\r\n" );
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document.write( ">>...Sets B and C have a total of 10 members in common...<<\r\n" );
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document.write( "The only regions common to B and C are the ones with x elements\r\n" );
document.write( "and y elements.  Since x=6, y must be 10-6 or 4.  So we put\r\n" );
document.write( "y=4 in there, like this:\r\n" );
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document.write( ">>...each members of set B is contained in at least one of the other two sets...<<\r\n" );
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document.write( "This tells us that the region with v in it has no elements at all, because\r\n" );
document.write( "if it had any elements, they would be members of B that were not contained\r\n" );
document.write( "in either of the other two sets, so therefore we know that v=0, so we\r\n" );
document.write( "write v=0 in that region:\r\n" );
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document.write( ">>...how many members are in set B?...<<\r\n" );
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document.write( "Now we know how many elements are in each of the regions of B,\r\n" );
document.write( "they are u,v,x,and y, and since we know that u=11, v=0, x=6, and\r\n" );
document.write( "y=4, then the number of elements in B is u+v+x+y = 11+0+6+4 = 21.\r\n" );
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document.write( "Answer: B has 21 elements.\r\n" );
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document.write( "Edwin

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