document.write( "Question 198484: please help thank so much.\r
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Algebra.Com's Answer #149040 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
A survey of a group of people produced the following results: there were 35 people with brown eyes and 24 people with blonde hair. If 14 people had both brown eyes and blonde hair and 27 people had neither, how many people were interviewed?\r
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document.write( "This is a Venn diagram problem.\r\n" );
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document.write( "First draw a big rectangle to hold all people interviewed:\r\n" );
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document.write( "Next draw a circle to hold all 35 people with brown eyes\r\n" );
document.write( "and label it E (for \"eyes\"):\r\n" );
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document.write( "Next draw a circle overlapping the first circle to \r\n" );
document.write( "hold all 24 people with blonde hair and label\r\n" );
document.write( "it H (for \"hair\"). \r\n" );
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document.write( "The overlapping part will contain the 14 people who had both\r\n" );
document.write( "brown eyes and blonde hair, so we write \"14\" in the region that's shaped\r\n" );
document.write( "like this \" () \", the overlapping region of the two \r\n" );
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document.write( "Now since 35 people had brown eyes, and 14 of those 35 are\r\n" );
document.write( "accounted for because they also had blonde hair. the rest\r\n" );
document.write( "of them, the other 35-14 or 21, are over in the left side of \r\n" );
document.write( "circle E.  So we write 21 in the left part of circle E.\r\n" );
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document.write( "Now since 24 people had blonde hair, and 14 of those 24 are\r\n" );
document.write( "accounted for because they also had brown eyes, the rest\r\n" );
document.write( "of them, the other 24-14 or 10, are over in the right side of \r\n" );
document.write( "circle H.  So we write 10 in the right part of circle H.\r\n" );
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document.write( "Now we have placed 21+14+10 or 45 of the people. So\r\n" );
document.write( "that leaves only the 27 people to be placed who had neither \r\n" );
document.write( "brown eyes nor brown hair.  They go in the rectangle outside \r\n" );
document.write( "both circles. I'll put those 27 people down on the bottom \r\n" );
document.write( "left side of the rectangle outside both circles:\r\n" );
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document.write( "Now all we need do is add up all the people in all the 4\r\n" );
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document.write( "21+14+10+27= 72\r\n" );
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document.write( "So there were 72 people interviewed.\r\n" );
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document.write( "Edwin

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