document.write( "Question 1189241: In a school of 970 students, all of them voted on two issues. 390 students voted in favour of banning cell phones, and 930 students voted in favour of having a school dance. Just 20 students voted against both issues. How many students voted in favour of both proposals \n" ); document.write( "

Algebra.Com's Answer #820551 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "In a school of 970 students, all of them voted on two issues.
\n" ); document.write( "390 students voted in favor of banning cell phones, and 930 students voted in favor of having a school dance.
\n" ); document.write( "Just 20 students voted against both issues. How many students voted in favor of both proposals
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document.write( "In this problem, we have a universal set W of all 970 students.\r\n" );
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document.write( "We also have three subsets: B (banning) of 390 students;\r\n" );
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document.write( "                            D (dance)   of 930 students,\r\n" );
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document.write( "                   and      A (against both) of 20 students.\r\n" );
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document.write( "Notice that the sub-sets B and D may have non-empty intersection; while the sub-set A is DISJOINT from both B and D.\r\n" );
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document.write( "THEREFORE, the union of B and D has  970 - 20 = 950 students.\r\n" );
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document.write( "So, we can write  n(B U D) = n(B) + n(D) - n(B & D),  or\r\n" );
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document.write( "                     950   = 390  + 930 -  n(B & D).\r\n" );
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document.write( "From this equation, you get the ANSWER to the problem's question  n(B & D) = 390 + 930 - 950 = 370.\r\n" );
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document.write( "ANSWER.  370 students voted in favor of both proposals.\r\n" );
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