document.write( "Question 226203: The value of a certain two-digit number is 9 times the sum of its digits. If the digits are reversed, the resulting number is 63 then the original number. Find the original number. \n" ); document.write( "

Algebra.Com's Answer #168511 by josmiceli(19441) $\"\"$ $\"About$

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Let the units digit be $\"u\"$
\n" ); document.write( "Let the tens digit be $\"t\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"10t+%2B+u+=+9%2A%28t+%2B+u%29\"$
\n" ); document.write( "(2) $\"10u+%2B+t+=+10t+%2B+u+-+63\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(1) $\"10t+%2B+u+=+9t+%2B+9u%29\"$
\n" ); document.write( " $\"t+=+8u\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"10u+%2B+t+=+10t+%2B+u+-+63\"$
\n" ); document.write( " $\"10u+%2B+8u+=+10%2A8u+%2B+u+-+63\"$
\n" ); document.write( " $\"18u+=+81u+-+63\"$
\n" ); document.write( " $\"81u+-+18u+=+63\"$
\n" ); document.write( " $\"63u+=+63\"$
\n" ); document.write( " $\"u+=+1\"$
\n" ); document.write( "and
\n" ); document.write( " $\"t+=+8u\"$
\n" ); document.write( " $\"t+=+8%2A1\"$
\n" ); document.write( " $\"t+=+8\"$
\n" ); document.write( "The original number is 81
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"10t+%2B+u+=+9%2A%28t+%2B+u%29\"$
\n" ); document.write( " $\"10%2A8+%2B+1+=+9%2A%288+%2B+1%29\"$
\n" ); document.write( " $\"81+=+9%2A9\"$
\n" ); document.write( " $\"81+=+81\"$
\n" ); document.write( "(2) $\"10u+%2B+t+=+10t+%2B+u+-+63\"$
\n" ); document.write( " $\"10%2A1+%2B+8+=+10%2A8+%2B+1+-+63\"$
\n" ); document.write( " $\"18+=+81+-+63\"$
\n" ); document.write( " $\"18+=+18\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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