document.write( "Question 1131572: There is a number that is called N. When N has a seven in front of it, the number formed is five times as large as when there is a seven after it. What is the smallest number of digits in N? \n" ); document.write( "

Algebra.Com's Answer #748257 by ikleyn(52812) $\"\"$ $\"About$

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document.write( "From the condition, N is the minimal whole number satisfying the equation\r\n" );
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document.write( "     =        (1)\r\n" );
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document.write( "for some integer positive \"n\".      It is equivalent to \r\n" );
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document.write( "      = 49N.\r\n" );
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document.write( "So, we need to find \"n\" in a way    is a multiple of  49.\r\n" );
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document.write( "The \"trying and error\" method, facilitated with Excel, quickly gives such a minimal  N = 14285, n = 5.\r\n" );
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document.write( "Check.  Left side of  eq(1)  is   = 714285.\r\n" );
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document.write( "       Right side of  eq(1)  is  5*(10*14285+7) = 714285.     ! Correct !\r\n" );
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document.write( "ANSWER.  The number is  14285.\r\n" );
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