document.write( "Question 1011629: The sum of the digits of a two digit number is 9. If the digits are reversed, the resulting number is 45 more than the original. What is the number? \n" ); document.write( "

Algebra.Com's Answer #627356 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Let a and b are 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( "Then you have the system of two equations for the unknowns a and b:\r
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\n" ); document.write( "\n" ); document.write( " $\"system%28a%2Bb+=+9%2C%0D%0A%0D%0A%2810b+%2Ba%29+-+%2810a+%2B+b%29+=+45%29\"$ .\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( " $\"system+%28a%2Bb=+9%2C%0D%0A%0D%0A9b+-+9a+=+45%29\"$ . \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( " $\"system+%28a%2Bb=+9%2C%0D%0A%0D%0Ab+-+a+=+5%29\"$ . \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=7, a=2.\r
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\n" ); document.write( "\n" ); document.write( "Hence, the number is 10a + b = 10*2+7 = 27.\r
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\n" ); document.write( "\n" ); document.write( "Answer. 27. \r
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\n" ); document.write( "\n" ); document.write( "For more problems of this type see the lesson Word problems on interchanging digits of numbers in this site.\r
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