document.write( "Question 1131957: When four positive integers are added three at a time, the sums are 1068, 1430. 1744, and 2013. What is the sum of the digits of the four original integers? \n" ); document.write( "

Algebra.Com's Answer #748708 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "Let the numbers be a, b, c, and d.  Then from the condition, you have these 4 equation for 4 unknowns\r\n" );
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document.write( "a + b + c     = 1068     (1)\r\n" );
document.write( "a + b     + d = 1430     (2)\r\n" );
document.write( "a     + c + d = 1744     (3)\r\n" );
document.write( "    b + c + d = 2013     (4)\r\n" );
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document.write( "Add the equation (1), (2), (3) and (4). You will get\r\n" );
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document.write( "3a + 3b + 3c + 3d = 1068 + 1430 + 1744 + 2013 = 6255.\r\n" );
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document.write( "Dividing both sides by 3, you get\r\n" );
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document.write( "a + b + c + d = 2085     (5)\r\n" );
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document.write( "Now subtract eq(1) from eq(5). You will get\r\n" );
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document.write( "d = 2085 - 1068 = 1017.\r\n" );
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document.write( "    Subtract eq(2) from eq(5). You will get\r\n" );
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document.write( "c = 2085 - 1430 =  655.\r\n" );
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document.write( "Similarly,\r\n" );
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document.write( "b = 2085 - 1744 = 341,\r\n" );
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document.write( "a = 2085 - 2013 =  72.\r\n" );
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document.write( "Now, when you have the numbers, you can easily calculate the sum of their digits.\r\n" );
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document.write( "Answer.  42.\r\n" );
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