document.write( "Question 1112120: Alan, Betty, and Cathy each have the same amount of money. How much money should Betty give to Alan and Cathy so that Alan has $5 more than Betty, and Cathy has $1 more than Alan? \n" ); document.write( "

Algebra.Com's Answer #727142 by ikleyn(52784) $\"\"$ $\"About$

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document.write( "Let M be the amount of money each person had initially.\r\n" );
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document.write( "Let A = amount Betty gave to Alan\r\n" );
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document.write( "Let C = amount Betty gave to Cathy.\r\n" );
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document.write( "Then Betty has  (M-A-C).\r\n" );
document.write( "     Alan  has  (M+A).\r\n" );
document.write( "     Cathy has  (M+C).\r\n" );
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document.write( "And the condition says\r\n" );
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document.write( "M - A - C = M + A - 5     (1)    ( . . . so that Alan has $5 more than Betty)\r\n" );
document.write( "M + C     = M + A - 1     (2)    ( . . . Cathy has $1 more than Alan)\r\n" );
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document.write( "Simplify by canceling M:\r\n" );
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document.write( "-A -C = A - 5             (1')\r\n" );
document.write( "C     = A - 1             (2')\r\n" );
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document.write( "Write in the standard form\r\n" );
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document.write( "2A + C = 5                (1'')\r\n" );
document.write( " A - C = 1                (2'')\r\n" );
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document.write( "Now add eq(1'')  and eq(2'').  You will get\r\n" );
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document.write( "3A = 6  ====>  A = 2.\r\n" );
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document.write( "Then from equation (2'')  C = A - 1 = 1.\r\n" );
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document.write( "Answer.   A = 2, C = 1.  In other words,  B gives 2 to A and B gives 1 to C.\r\n" );
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document.write( "Check.    Do the check on your own.\r\n" );
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\n" ); document.write( "Comment from student:   Thank you for #1112120
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\n" ); document.write( "\n" ); document.write( "My response:   I want to commend you for two things:\r
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\n" ); document.write( "\n" ); document.write( "            a) for sending your \"Thanks\",   and\r
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\n" ); document.write( "\n" ); document.write( "            b) for referring to the problem ID number.\r
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\n" ); document.write( "\n" ); document.write( "Most of other users/\"students\" are so badly educated people that allow themselves do neither a) nor b).\r
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