document.write( "Question 1166702: i am a number between 200 and 300. THE SUM OF MY DIGITS IS 10. if you add me to my reversed digits, i am equal to 767. what number could i be? \n" ); document.write( "

Algebra.Com's Answer #791217 by ikleyn(52879) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "First digit of the number is 2.\r\n" );
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document.write( "If the last digit is x, then adding the number with the reversed one and looking into the last digit of the sum, we have this equation\r\n" );
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document.write( "    2 + x = 7.\r\n" );
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document.write( "So, we conclude that the last digit of the number is x = 7-2 = 5.\r\n" );
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document.write( "Thus the unknown number is  of the form  2t5,  where t is the tens digit.\r\n" );
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document.write( "Next, adding   2t5         (original number)\r\n" );
document.write( "               5t2         (reversed number)\r\n" );
document.write( "            -----------\r\n" );
document.write( "               767\r\n" );
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document.write( "we conclude that  t+t = 2t = 6, which implies  t = 3.\r\n" );
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document.write( "ANSWER.  The number is  235.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that the sum of digits in my number is 2+3+5 = 10, as stated.\r
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\n" ); document.write( "\n" ); document.write( "But in my solution, I did not use this fact.\r
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\n" ); document.write( "\n" ); document.write( "So, this condition is excessive and is not necessary for the solution.\r
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\n" ); document.write( "\n" ); document.write( "If such excessive condition is valid, then it is CONSISTENT with the answer, as we see it in this case.\r
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\n" ); document.write( "\n" ); document.write( "Had it be not valid by the observation, it would contradict the solution (which is not the case).\r
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\n" ); document.write( "\n" ); document.write( "So, you should be careful with such additional excessive statements and check them after completing your analysis
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