document.write( "Question 1135339: In a town, 80% of the houses have water and 34% of the houses have no electricity. A quarter of the houses with water have no electricity. What percetage of the houses have neither water nor elecricity? \n" ); document.write( "

Algebra.Com's Answer #752973 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let H be the number of houses in the town.\r\n" );
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document.write( "In this problem, we are given\r\n" );
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document.write( "a)  the set of the houses in the town that HAVE WATER (80% of all houses of the town).  Let's call this set W.\r\n" );
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document.write( "b)  the set of the houses in the town that HAVE NO ELECTRICITY (34% of all houses of the town).  Let's call this set NE.\r\n" );
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document.write( "c)  also, we know that \"A quarter of the houses with water have no electricity\".\r\n" );
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document.write( "    In other words, 0.25*(0.8*H) = 0.2H houses belong to the intersection  (W n NE).\r\n" );
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document.write( "The question is how many houses is in the set  NE \ (W n NE).    (<<<---=== the difference of the set NE and its subset (W n NE)  ).\r\n" );
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document.write( "Obviously, the answer is  0.34H - 0.2H = 0.14H.\r\n" );
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document.write( "Thus the answer to the problem's question is 14%.\r\n" );
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