document.write( "Question 548396: The four numbers a < b < c < d can be paired in six different ways. if each pair has a different sum, and if the four smallest sums are 1,2,3 and 4, what are all possible values of d \n" ); document.write( "

Algebra.Com's Answer #357004 by Edwin McCravy(20056) $\"\"$ $\"About$

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The four numbers a < b < c < d can be paired in six different ways. if each pair has a different sum, and if the four smallest sums are 1,2,3 and 4, what are all possible values of d?
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document.write( "The three smallest sums are \r\n" );
document.write( "a+b, which is 1.\r\n" );
document.write( "a+c, which is 2.\r\n" );
document.write( "b+c, which is 3.\r\n" );
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document.write( "The next larger sum is a+d=4\r\n" );
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document.write( "We solve this system of 3 equations in 3 unknowns:\r\n" );
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document.write( "a + b     = 1\r\n" );
document.write( "a     + c = 2\r\n" );
document.write( "    b + c = 3\r\n" );
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document.write( "and get a=0, b=1, and c=2\r\n" );
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document.write( "Since we know that \r\n" );
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document.write( "a + d = 4\r\n" );
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document.write( "we substitute 0 for a, and get:\r\n" );
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document.write( "0 + d = 4\r\n" );
document.write( "    d = 4\r\n" );
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document.write( "So the only values possible are a=0, b=1, c=2, and d = 4\r\n" );
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document.write( "Answer: d can only be 4.\r\n" );
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document.write( "Edwin

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