document.write( "Question 843052: If A gives B £2 they will have the same amount of money, and if B gives A £2 then A will have twice as much as B.\r
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Algebra.Com's Answer #507915 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
If A gives B £2 they will have the same amount of money, and if B gives A £2 then A will have twice as much as B.
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document.write( "Suppose A begins with £a and B begins with £b \r\n" );
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document.write( "If A gives B £2, then A will have £(a-2) and B will have £(b+2).\r\n" );
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document.write( "In that case their amounts would be equal, so we set them equal:\r\n" );
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document.write( "                 £(a-2) = £(b+2)\r\n" );
document.write( "                    a-2 = b+2\r\n" );
document.write( "                      a = b+4\r\n" );
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document.write( "If B gives A £2, then B will have £(b-2) and A will have £(a+2).\r\n" );
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document.write( "In that case A's amount would be twice B's amount, so we have:\r\n" );
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document.write( "                 £(a+2) = 2·£(b-2)\r\n" );
document.write( "                    a+2 = 2(b-2)\r\n" );
document.write( "                    a+2 = 2b-4\r\n" );
document.write( "                      a = 2b-6\r\n" );
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document.write( "So we have this system of 2 equations in two unknowns:\r\n" );
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document.write( "                     \"system%28a=b%2B4%2Ca=2b-6%29\"\r\n" );
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document.write( "                     b+4 = 2b-6\r\n" );
document.write( "                      10 = b\r\n" );
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document.write( "                       a = 2b-6 = 2(10)-6 = 20+6 = 14\r\n" );
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document.write( "So A has £14 and B has £10\r\n" );
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document.write( "Checking:  If A gives B £2, A will have only £12 and B will have £12. \r\n" );
document.write( "That checks because they are the same.  If B gives A £2, B will have only £8\r\n" );
document.write( "and A will have £16. That checks because £16 is twice as much as £8.\r\n" );
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document.write( "Edwin

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