document.write( "Question 1203099: If we place a 3 at both ends of a number, its value is increased by 3372. Find the original number. \n" ); document.write( "

Algebra.Com's Answer #838385 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If we place a 3 at both ends of an $\"highlight%28integer%29\"$ number, its value is increased by 3372.
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document.write( "Let the original integer number be x.\r\n" );
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document.write( "It is almost obvious (and easy to show) that the original number is a two-digit number.\r\n" );
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document.write( "If we place a 3 at both ends of such a number, its value becomes  3000+10x+3.\r\n" );
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document.write( "Therefore, according to the condition, we should find x from this equation\r\n" );
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document.write( "    (3000 + 10x + 3) - x = 3372.\r\n" );
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document.write( "It is easy\r\n" );
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document.write( "    10x - x = 3372 - 3000 - 3\r\n" );
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document.write( "       9x  = 369\r\n" );
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document.write( "         x  =  369/9 = 41.\r\n" );
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document.write( "CHECK.  3413 - 41 = 3372, the increase value.   ! correct !\r\n" );
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document.write( "ANSWER.  The original number is 41.\r\n" );
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