document.write( "Question 1084534: If n(A∪B)=40, n(A∩B)=10 and n(A)=15, find n(B) \n" ); document.write( "
Algebra.Com's Answer #698622 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "By Venn diagram:\r\n" );
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document.write( "n(A∪B) = x + y + z = 40, \r\n" );
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document.write( "n(A∩B) = y = 10 \r\n" );
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document.write( "n(A) = x + y = 15\r\n" );
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document.write( "n(B) = y + z = ?\r\n" );
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document.write( "So the system of equations is:\r\n" );
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document.write( "(eq. 1)              x + y + z = 40\r\n" );
document.write( "(eq. 2)                  y     = 10\r\n" );
document.write( "(eq. 3)              x + y     = 15\r\n" );
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document.write( "Subtract (eq. 3) minus (eq. 2)\r\n" );
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document.write( " (eq. 3)              x + y     =  15\r\n" );
document.write( "-(eq. 2)                 -y     = -10\r\n" );
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document.write( "                      x         =  5\r\n" );
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document.write( "Subtract (eq. 1) minus (eq. 3)\r\n" );
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document.write( " (eq. 1)              x + y + z =  40\r\n" );
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document.write( "-(eq. 3)             -x - y     = -15\r\n" );
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document.write( "                              z =  25\r\n" );
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document.write( "Substitute x = 5 in (eq. 3)\r\n" );
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document.write( " (eq. 3)              5 + y     =  15  \r\n" );
document.write( "                          y     =  10\r\n" );
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document.write( "n(B) = y + z = 10 + 25 = 35\r\n" );
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document.write( "By formula\r\n" );
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document.write( "n(A∪B) = n(A) + n(B) - n(A∩B) \r\n" );
document.write( "  40   =  15  + n(B) -  10\r\n" );
document.write( "  40   =   5  + n(B)\r\n" );
document.write( "  35   =  n(B)\r\n" );
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document.write( "It's easier to use the formula, but you don't learn \r\n" );
document.write( "what's going on unless you understand the Venn diagram\r\n" );
document.write( "method.\r\n" );
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document.write( "Edwin

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