document.write( "Question 1148826: Martha is Esther's mother..Martha and Esther's age have the same digits but in reverse order. In 13 years, Martha will be twice as old as Esther. How old is Esther now \n" ); document.write( "

Algebra.Com's Answer #770164 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Let E = 10a + b be Esher's age.\r\n" );
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document.write( "    So, the number E has the tens digit \"a\" and the ones digit \"b\".\r\n" );
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document.write( "Let M be the Marta's age.\r\n" );
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document.write( "    From the condition, we know that the Marta's age is M = 10b+a, the reversed number to the Esher's age.\r\n" );
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document.write( "We also are given that\r\n" );
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document.write( "    M + 13 = 2*(E+13),\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    M = 2E + 13.\r\n" );
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document.write( "Using the decimal forms of the numbers E and M, it means that\r\n" );
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document.write( "    10b + a = 20a + 2b + 13,   or\r\n" );
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document.write( "    8b - 19a = 13.    (1)\r\n" );
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document.write( "So, from the condition, we have ONLY ONE equation for two unknown digits \"a\" and \"b\", equation (1).\r\n" );
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document.write( "But we also know that a\" and \"b\" are INTEGER numbers between 1 and 9 each.\r\n" );
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document.write( "At this point, you can write  b =   and  search for those integer \"a\" that produce integer values of \"b\".\r\n" );
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document.write( "It is easy to do in Excel.\r\n" );
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document.write( "In this way, I found  a= 1, b= 4.\r\n" );
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document.write( "So, the Esther age is 14 years, while Marta's age is 41 years.     ANSWER\r\n" );
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document.write( "You can check, on your own, that all requirements of the condition are satisfied.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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