document.write( "Question 1000123: a number is made of two digit. the sum of the digit is 11. if the digit is interchange the original number is increased by 9. find the numbers. \n" ); document.write( "
Algebra.Com's Answer #617610 by ikleyn(52946)\"\" \"About 
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\n" ); document.write( "Answer. 56.\r
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\n" ); document.write( "\n" ); document.write( "Let  a  and  b  be the digits of your number  n,  so that  n = 10a + b.\r
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\n" ); document.write( "\n" ); document.write( "The number after interchanging digits is  10b + a.\r
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\n" ); document.write( "\n" ); document.write( "Thus you have the system of two equations for the unknowns  a  and  b:\r
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\n" ); document.write( "\n" ); document.write( "\"system%28a%2Bb+=+11%2C%0D%0A%0D%0A%2810b+%2Ba%29+-+%2810a+%2B+b%29+=+9%29\".\r
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\n" ); document.write( "\n" ); document.write( "Now,  simplify it:\r
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\n" ); document.write( "\n" ); document.write( "\"system+%28a%2Bb=+11%2C%0D%0A%0D%0A9b+-+9a+=+9%29\". \r
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\n" ); document.write( "\n" ); document.write( "Simplify it one more time:\r
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\n" ); document.write( "\n" ); document.write( "\"system+%28a%2Bb=+11%2C%0D%0A%0D%0Ab+-+a+=+1%29\". \r
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\n" ); document.write( "\n" ); document.write( "Solve it.\r
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\n" ); document.write( "\n" ); document.write( "The solution is   b=6,  a=5.\r
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\n" ); document.write( "\n" ); document.write( "Hence,  the number is  10a + b = 10*5+6 = 56.\r
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