document.write( "Question 940084: Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and
\n" ); document.write( "B. Is this data correct? Explain. \n" ); document.write( "

Algebra.Com's Answer #572939 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "

The red circle represents all the car owners that own car A.\r\n" );
document.write( "The red circle is made up of region w and region x.\r\n" );
document.write( "\r\n" );
document.write( "The blue circle represents all the car owners that own car B.\r\n" );
document.write( "The blue circle is made up of region x and region y.\r\n" );
document.write( "\r\n" );
document.write( "So you see that region x is part of both circle A and B.\r\n" );
document.write( "Region w is part of circle A but it is NOT part of circle B.\r\n" );
document.write( "Region y is part of circle B but it is NOT part of circle A.\r\n" );
document.write( "\r\n" );
document.write( "Therefore \r\n" );
document.write( "\r\n" );
document.write( "Region x represents the 50 car owners that own both cars\r\n" );
document.write( "A and B.  \r\n" );
document.write( "Region w represents the car owners that own car A but DO NOT\r\n" );
document.write( "own car B.\r\n" );
document.write( "Region y represents the car owners that own car B but DO NOT\r\n" );
document.write( "own car A.\r\n" );
document.write( "Region z (the area outside the circles but inside the rectangle.\r\n" );
document.write( "\r\n" );
document.write( "Region z represents the car owners that DO NOT own car A and\r\n" );
document.write( "also DO NOT own car B.\r\n" );
document.write( "\r\n" );
document.write( "Therefore we will put the number 50 for region x, since 50 own\r\n" );
document.write( "both car A and car B.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We are told that 400 owned car A, and the region that contains 50\r\n" );
document.write( "is part of circle A, so the remaining 400-50=350 that are in circle\r\n" );
document.write( "A go in region w, so we put 350 in region w: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We are told that 200 owned car B, and the region that contains 50\r\n" );
document.write( "is part of circle B, so the remaining 200-50=150 that are in circle\r\n" );
document.write( "B go in region y, so we put 150 in region y:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Now we see that something is wrong, because we were told that\r\n" );
document.write( "there were only 500 car owners investigated and we already\r\n" );
document.write( "have 350+50+150 = 550.  So the data we are given is contradictory.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );