document.write( "Question 183641: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. WHat is the original number? \n" ); document.write( "

Algebra.Com's Answer #137858 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"t\"$ = the tens digit of the original number
\n" ); document.write( "Let $\"u\"$ = the units digit of the original number
\n" ); document.write( "given:
\n" ); document.write( "The original number is $\"10t+%2B+u\"$
\n" ); document.write( "The number with the digits reversed is $\"10u+%2B+t\"$
\n" ); document.write( "(1) $\"10u+%2B+t+=+10t+%2B+u+%2B+9\"$
\n" ); document.write( "(2) $\"u+%2B+t+=+11\"$
\n" ); document.write( "---------------------
\n" ); document.write( "From (1)
\n" ); document.write( "(1) $\"10u+%2B+t+=+10t+%2B+u+%2B+9\"$
\n" ); document.write( "(1) $\"10u+-+u+%2B+t+-+10t+=+9\"$
\n" ); document.write( "(1) $\"9u+-+9t+=+9\"$
\n" ); document.write( "(1) $\"u+-+t+=+1\"$
\n" ); document.write( "Add (1) and (2)
\n" ); document.write( "(2) $\"u+%2B+t+=+11\"$
\n" ); document.write( "(1) $\"u+-+t+=+1\"$
\n" ); document.write( "(3) $\"2u+=+12\"$
\n" ); document.write( " $\"u+=+6\"$
\n" ); document.write( "And, since
\n" ); document.write( "(2) $\"u+%2B+t+=+11\"$
\n" ); document.write( "(2) $\"6+%2B+t+=+11\"$
\n" ); document.write( "(2) $\"t+=+5\"$
\n" ); document.write( "The original number is 56
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"10u+%2B+t+=+10t+%2B+u+%2B+9\"$
\n" ); document.write( "(1) $\"60+%2B+5+=+50+%2B+6+%2B+9\"$
\n" ); document.write( "(1) $\"65+=+65\"$
\n" ); document.write( "(2) $\"u+%2B+t+=+11\"$
\n" ); document.write( "(2) $\"6+%2B+5+=+11\"$
\n" ); document.write( "(2) $\"11+=+11\"$
\n" ); document.write( "OK \n" ); document.write( "

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