document.write( "Question 1101027: Parcel A and B together weigh 24 kgs, but parcel B and C together weighs only 21 kgs. When parcel A and C are paired, the combined weight is 27kgs. If the weight of parcel A is represented by a, parcel B by b and parcel C by c; derive a system of three equations for a, b and c. Using the inverse method derive the combined weight of parcel A, B and C. \n" ); document.write( "

Algebra.Com's Answer #715607 by ikleyn(52802) $\"\"$ $\"About$

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document.write( "a + b = 24,     (1)\r\n" );
document.write( "b + c = 21,     (2)\r\n" );
document.write( "a + c = 27.     (3)\r\n" );
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document.write( "Add all the three eqs (1), (2) and (3)  (both sides).\r\n" );
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document.write( "You will get\r\n" );
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document.write( "2a + 2b + 2c = 24+21+27,   or\r\n" );
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document.write( "2(a + b + c)  = 72,        which implies\r\n" );
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document.write( "a + b + c = 36.    (4)\r\n" );
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document.write( "Now      subtract eq(1) from eq(4) (both sides). You will get  c = 36-24 = 12.\r\n" );
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document.write( "Next     subtract eq(2) from eq(4) (both sides). You will get  a = 36-21 = 15.\r\n" );
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document.write( "Finally, subtract eq(3) from eq(4) (both sides). You will get  b = 36-27 = 9.\r\n" );
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document.write( "It is  THE STANDARD METHOD  for solving problems like this.\r\n" );
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document.write( "The problem asks: \"Using the inverse method derive the combined weight of parcel A, B and C.\"\r\n" );
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document.write( "For me, this formulation, if to interpret each word literally, makes no sense.\r\n" );
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document.write( "But in any case, in my previous solution above I derived the expression\r\n" );
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document.write( "a + b + c = 36    (equation (4) ).\r\n" );
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document.write( "I didn't use any inverse method for it.\r\n" );
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document.write( "I simply added the three equations (1),(2) and (3),  then divided the result by 2.\r\n" );
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\n" ); document.write( "The method of solvinng such problems was described in my lesson\r
\n" ); document.write( "\n" ); document.write( " - The tricks to solve some word problems with three and more unknowns using mental math\r
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