document.write( "Question 265920: My entire nickel and dime collection is housed in my cardboard box collection, which consists of exactly 24 boxes. 13 of the boxes contain nickels, 8 contain dimes and 5 contain both nickels and dimes. How many of the boxes contain neither
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Algebra.Com's Answer #195439 by Edwin McCravy(20086) $\"\"$ $\"About$

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My entire nickel and dime collection is housed in my cardboard box collection, which consists of exactly 24 boxes. 13 of the boxes contain nickels, 8 contain dimes and 5 contain both nickels and dimes. How many of the boxes contain neither\r
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document.write( "We will draw what is called a \"Venn diagram\":\r\n" );
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document.write( "First draw a big rectangle to contain all 24 boxes.\r\n" );
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document.write( "Now in that rectangle draw a big circle for the 13 boxes that\r\n" );
document.write( "contain nickels and label it N:\r\n" );
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document.write( "Next draw another big circle overlapping it to contain the 8 boxes\r\n" );
document.write( "that contain dimes and label it D:\r\n" );
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document.write( "Now the 5 boxes which contain both nickels and dimes will have to go\r\n" );
document.write( "in the overlapping part of those two circles.  So we'll write  \r\n" );
document.write( "in there to represent the 5 boxes in that region.  Those 5 have to\r\n" );
document.write( "be in BOTH CIRCLES at the same time! The way for those 5 to be in both\r\n" );
document.write( "circles at the same time is for them to be in the overlapping part of the\r\n" );
document.write( "two circles, which is football-shaped:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Since there are 13 boxes which contain nickels, the rest of those 13 \r\n" );
document.write( "boxes besides the 5 that contain both nickels and dimes, that is, \r\n" );
document.write( "13-5, or 8, will have to go in this region, which is moon-shaped,\r\n" );
document.write( "in which we write 8:\r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Notice that the circle labeled N now contains the 13 boxes which\r\n" );
document.write( "contain nickels, 8 of them in the left moon-shaped part of the\r\n" );
document.write( "circle and 5 in the football-shaped part of the circle.  The 8\r\n" );
document.write( "contain nickels only and the 5 contain both nickels and dimes. \r\n" );
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document.write( "Since there are 8 boxes which contain dimes, the rest of those 8 \r\n" );
document.write( "besides the 5 that are in both circles, that is, 8-5, or 3, will \r\n" );
document.write( "be in the right moon-shaped region, in which we write 3:\r\n" );
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document.write( "`                      `  \r\n" );
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document.write( "and in the main drawing:\r\n" );
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document.write( "Notice that the circle labeled D now contains the 8 boxes which\r\n" );
document.write( "contain dimess, 3 of them in the right moon-shaped part of the\r\n" );
document.write( "circle and 5 in the football-shaped part of the circle.  The 3\r\n" );
document.write( "contain dimes only and the 5 contain both nickels and dimes. \r\n" );
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document.write( "Now we have accounted for 8 + 5 + 3 or 16 of the 24 boxes.  That\r\n" );
document.write( "leaves 24-16, or 8 boxes which contain neither nickels nor dimes,\r\n" );
document.write( "and so those 8 are outside the two circles, like this:\r\n" );
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document.write( "So the answer is 8.\r\n" );
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document.write( "Edwin

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