document.write( "Question 612737: Four integers, added 3 at a time, produce the following sums: 72, 84, 96, and 108. What is the sum of all 4 integers? \n" ); document.write( "
Algebra.Com's Answer #385701 by Edwin McCravy(20060)\"\" \"About 
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Four integers, added 3 at a time, produce the following sums: 72, 84, 96, and 108. What is the sum of all 4 integers?
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document.write( "Suppose they are a,b,c,and d, then their sums taken 3 at at time\r\n" );
document.write( "are   \r\n" );
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document.write( "a + b + c =  72\r\n" );
document.write( "a + b + d =  84\r\n" );
document.write( "a + c + d =  96\r\n" );
document.write( "b + c + d = 108\r\n" );
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document.write( "Let's line up all 4 or those equations and add them:\r\n" );
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document.write( " a +  b +  c      =  72\r\n" );
document.write( " a +  b      +  d =  84\r\n" );
document.write( " a      +  c +  d =  96\r\n" );
document.write( "      b +  c +  d = 108\r\n" );
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document.write( "3a + 3b + 3c + 3d = 360\r\n" );
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document.write( "Divide through by 3\r\n" );
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document.write( "    a + b + c + d = 120\r\n" );
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document.write( "That's the answer you were asked for.  \r\n" );
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document.write( "But we still don't know what those four integers are.\r\n" );
document.write( "And they could have asked you that.\r\n" );
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document.write( "The given numbers 72, 84, 96, and 108 are consecutive \r\n" );
document.write( "multiples of 12, in fact they are:\r\n" );
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document.write( "6×12, 7×12, 8×12, 9×12\r\n" );
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document.write( "So if we can find 4 smaller integers which when added 3 at a time,\r\n" );
document.write( "produce the sums: 6, 7, 8 and 9, then we can think of them in\r\n" );
document.write( "\"dozens\" and multiply them by 12, and they will produce the 4 sums\r\n" );
document.write( "above.\r\n" );
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document.write( "The smallest three integers 1,2, and 3 have sum 1+2+3 = 6\r\n" );
document.write( "So 1+2+4 = 7, 1+3+4 = 8, and 2+3+4 = 9, so\r\n" );
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document.write( "1,2,3,4 when added 3 at a time, produce the sums: 6, 7, 8 and 9,\r\n" );
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document.write( "Multiplying them by 12, we have the integers 12, 24. 36, and 48.\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "12+24+36 =  72\r\n" );
document.write( "12+24+48 =  84\r\n" );
document.write( "12+36+48 =  96\r\n" );
document.write( "24+36+48 = 108 \r\n" );
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document.write( "And their sum is 12+24+36+48 =  120.\r\n" );
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document.write( "Edwin
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