document.write( "Question 1206529: a survey of 220 families showed that: 63 had a dog; 64 had a cat; 28 had a dog and a cat; 84 neither had a cat nor a dog and in addition did not have a parakeet; 6 had a cat, a dog and a parakeet. how many families had a parakeet only? \n" ); document.write( "

Algebra.Com's Answer #844077 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a survey of 220 families showed that:
\n" ); document.write( "63 had a dog; 64 had a cat; 28 had a dog and a cat;
\n" ); document.write( "84 neither had a cat nor a dog and in addition did not have a parakeet;
\n" ); document.write( "6 had a cat, a dog and a parakeet.
\n" ); document.write( "how many families had a parakeet only?
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document.write( "We have a universal set of 220 families and three its basic subsets\r\n" );
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document.write( "    d  of 63 families having a dog;\r\n" );
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document.write( "    c  of 64 families having a cat;\r\n" );
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document.write( "    p  of unknown number of families having a parakeet.\r\n" );
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document.write( "The number of families in the union (d U c) is  63 + 64 - 28 = 99.\r\n" );
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document.write( "The set of families that neither have a cat nor a dog  is the complement to the set (d U c),\r\n" );
document.write( "and the number of such families is  220 - 99 = 121.\r\n" );
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document.write( "We are told, that the number of families that \"in addition\" do not have parakeet is 84.\r\n" );
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document.write( "From it, we conclude that  121-84 = 37  families do have a parakeet, but have neither a cat nor a dog.\r\n" );
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document.write( "So, the answer to the problem's question is 37 families.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the last condition in the post\r
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document.write( "    \"6 had a cat, a dog and a parakeet. \"\r\n" );
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is excessive and unnecessary. I did not use it in my solution.\r
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\n" ); document.write( "\n" ); document.write( "This problem is DEFINITELY not to write and/or to use Venn diagram
\n" ); document.write( "and accompanied system of linear equations in 8 unknowns.\r
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\n" ); document.write( "\n" ); document.write( "This problem's true destination and true purpose is to solve it MENTALLY
\n" ); document.write( "and to teach young students to think logically about the sets and their subsets.\r
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