document.write( "Question 1033974: In a village, out of 120 farmers, 93 farmers have grown
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Algebra.Com's Answer #648584 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Notice how many farmers are in each of the 8 \r\n" );
document.write( "regions and what they have and/or have not grown:\r\n" );
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document.write( "\"a\" farmers have grown vegetables but have not\r\n" );
document.write( "grown flowers or sugar cane.\r\n" );
document.write( "\"b\" farmers have grown Vegetables and flowers but\r\n" );
document.write( "have not grown sugar cane.\r\n" );
document.write( "\"c\" farmers have grown flowers but have not grown\r\n" );
document.write( "vegetables or sugar cane.\r\n" );
document.write( "\"d\" farmers have grown Vegetables and sugarcane \r\n" );
document.write( "but have not grown flowers.\r\n" );
document.write( "\"x\" farmers have grown all three. That's the number\r\n" );
document.write( "we are wanting to find.\r\n" );
document.write( "\"e\" farmers have grown flowers and sugarcane but\r\n" );
document.write( "have not grown vegetables.\r\n" );
document.write( "\"g\" farmers have grown sugarcane but have not \r\n" );
document.write( "grown vegetables or flowers.\r\n" );
document.write( "\"h\" farmers have not grown any of the three things\r\n" );
document.write( "(perhaps they have only grown fruit and/or cotton).\r\n" );
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document.write( "Let x = the answer, the number who have grown all\r\n" );
document.write( "three. That's the region right in the center that\r\n" );
document.write( "is common to all three.\r\n" );
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\n" ); document.write( "27 farmers have grown vegetables & sugarcane.
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document.write( "d+x = 27\r\n" );
document.write( "d = 27-x\r\n" );
document.write( "So we write 27-x for d\r\n" );
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\n" ); document.write( "24 farmers have grown flowers & sugarcane,
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document.write( "e+x = 24\r\n" );
document.write( "e = 24-x\r\n" );
document.write( "So we write 24-x for e\r\n" );
document.write( "

\n" ); document.write( "45 farmers have grown vegetables & flowers,
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document.write( "b+x = 45\r\n" );
document.write( "b = 45-x\r\n" );
document.write( "So we write 45-x for b\r\n" );
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document.write( "d+x+e+g = 45\r\n" );
document.write( "Substituting d=27-x, e=24-x,\r\n" );
document.write( "27-x+x+24-x+g = 45\r\n" );
document.write( "51-x+g = 45\r\n" );
document.write( "g = x-6\r\n" );
document.write( "So we write x-6 for g\r\n" );
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document.write( "b+c+x+e = 63\r\n" );
document.write( "Substituting b=45-x, e=24-x,\r\n" );
document.write( "45-x+c+x+24-x = 63\r\n" );
document.write( "69-x+c = 63\r\n" );
document.write( "c = x-6\r\n" );
document.write( "So we write x-6 for c, also\r\n" );
document.write( "

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document.write( "a+b+d+x = 93\r\n" );
document.write( "Substituting b=45-x, d=27-x, \r\n" );
document.write( "a+45-x+27-x+x = 93\r\n" );
document.write( "a+72-x = 93\r\n" );
document.write( "a = x+21\r\n" );
document.write( "So we write x+21 for a\r\n" );
document.write( "

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document.write( "a+b+c+d+x+e+g+h = 120\r\n" );
document.write( "Substituting a=x+21, b=45-x, c=x-6,\r\n" );
document.write( "d=27-x, e=24-x, g=x-6, \r\n" );
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document.write( "x+21+45-x+x-6+x+27-x+x+24-x+x-6+h = 120\r\n" );
document.write( "x+105+h = 120\r\n" );
document.write( "x+h = 15\r\n" );
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document.write( "So the number of farmers who planted either all of\r\n" );
document.write( "the three or none of the three totals 15.\r\n" );
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document.write( "Therefore, since you state that the correct answer\r\n" );
document.write( "is 15, that means that there were no farmers who\r\n" );
document.write( "planted none of them.   \r\n" );
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document.write( "The problem should have stated that, because it is\r\n" );
document.write( "very feasible that some of the farmers might \r\n" );
document.write( "not have planted either vegetables, flowers or\r\n" );
document.write( "sugarcane, but only fruit and/or cotton.  Or, they\r\n" );
document.write( "could have only raised chickens and cows!\r\n" );
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document.write( "So obviously we are assuming h=0.  And when, but ONLY\r\n" );
document.write( "when we do, does x=15.\r\n" );
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document.write( "You should point out to your teacher that it should\r\n" );
document.write( "have been stated that all farmers planted at least\r\n" );
document.write( "one of the three.  Otherwise we cannot know that h=0.\r\n" );
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document.write( "Edwin

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