document.write( "Question 999050: Four numbers, taken two at a time, give the sums 84, 88, 100, 100, 112 and 116. What are the four numbers? \n" ); document.write( "

Algebra.Com's Answer #616737 by ikleyn(52855) $\"\"$ $\"About$

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\n" ); document.write( "Four numbers, taken two at a time, give the sums 84, 88, 100, 100, 112 and 116. What are the four numbers?
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document.write( "GIVEN:\r\n" );
document.write( "A+B=84\r\n" );
document.write( "A+C=88\r\n" );
document.write( "A+D=100\r\n" );
document.write( "B+C=100\r\n" );
document.write( "B+D=112\r\n" );
document.write( "C+D=116\r\n" );
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document.write( "Let us consider those sums that relate to 3 numbers A, B and C:\r\n" );
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document.write( "A+B=84     (1)\r\n" );
document.write( "A+C=88     (2)\r\n" );
document.write( "B+C=100    (3)\r\n" );
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document.write( "Sum up the left and the right sides. You will get\r\n" );
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document.write( "2*(A + B + C) = 84 + 88 + 100 = 272. It gives \r\n" );
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document.write( "A + B + C =  = 136   (4).\r\n" );
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document.write( "Now, distract (1) from (4). You will get\r\n" );
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document.write( "C = 136 - 84 = 52.\r\n" );
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document.write( "Distract (2) from (4). You will get\r\n" );
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document.write( "B = 136 - 88 = 48.\r\n" );
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document.write( "Distract (3) from (4). You will get\r\n" );
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document.write( "A = 136 - 100 = 36.\r\n" );
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document.write( "Now you can easily determine D from A+D=100, for instance:\r\n" );
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document.write( "D = 100 - 36 = 64.\r\n" );
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document.write( "Answer. A=36, B=48, C=52, D=64.\r\n" );
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document.write( "Notice. We have 4 unknowns, therefore 4 equations is enough to find the unknowns. The rest of equations are excessive. \r\n" );
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