document.write( "Question 552895: The sum of the digits of a two-digit number is 15. If the digits are reversed, the number is increased by 9. What is the original number? \n" ); document.write( "

Algebra.Com's Answer #360558 by KMST(5328) $\"\"$ $\"About$

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Let x be the tens digit, and y the ones digit
\n" ); document.write( "The number's value is
\n" ); document.write( " $\"10x%2By\"$ , while the value of the number with the digits reversed is
\n" ); document.write( " $\"10y%2Bx\"$
\n" ); document.write( "We know that $\"x%2By=15\"$ and that
\n" ); document.write( " $\"10y%2Bx=%2810x%2By%29%2B9\"$ --> $\"10y%2Bx=10x%2By%2B9\"$ --> $\"9y-9x=9\"$ --> $\"9%28y-x%29=9\"$ $\"y-x=1\"$
\n" ); document.write( "We solve the system
\n" ); document.write( " $\"x%2By=15\"$
\n" ); document.write( " $\"-x%2By=1\"$
\n" ); document.write( "any way we can to find $\"y=8\"$ and $\"x=7\"$
\n" ); document.write( "So the original number is 78. \n" ); document.write( "

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