document.write( "Question 1175680: An automobile factory needs to select other companies as suppliers for 3 different parts. The factory contacted a number of companies and found that some companies produce 1 needed item, some produce 2, and others produce 3 needed items. 35 companies produce part A, 24 produce part B, and 27 produce part C. 12 companies produce both parts A and B, 19 produce part B and C, and 13 produce part A and C, and 9 produce all 3 parts. What was the total number of companies contacted? \n" ); document.write( "

Algebra.Com's Answer #801330 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Let  X  be the set of companies that produce item A;\r\n" );
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document.write( "     Y  be the set of companies that produce item B;\r\n" );
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document.write( "     Z  be the set of companies that produce item C.\r\n" );
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document.write( "You are given the numbers of elements  n(X), n(Y), n(Z),\r\n" );
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document.write( "numbers of elements in all in-pair intersections n(XY), n(XZ), n(YZ);\r\n" );
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document.write( "and the number of elements in the triple intersection n(XYZ).\r\n" );
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document.write( "They want you find n(X U Y U Z).\r\n" );
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document.write( "Use the formula\r\n" );
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document.write( "    n(X U Y U Z) = n(X) + n(Y) + n(Z) - n(XY - n(XZ) - n(YZ) + n(XYZ) = \r\n" );
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document.write( "                 = 35 + 24 + 27 - 12 - 19 - 13 + 9 = 51.\r\n" );
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document.write( "ANSWER.  51 companies were contacted.\r\n" );
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