document.write( "Question 803222: A number consists of two digits whose sum is 9. the number formed by reversing the digits exceeds twice the original number by 18. find the original number.
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Algebra.Com's Answer #484189 by josmiceli(19441) $\"\"$ $\"About$

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Let the tens digit = $\"+t+\"$
\n" ); document.write( "Let the units digit = $\"+u+\"$
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\n" ); document.write( "'(1) $\"+t+%2B+u+=+9+\"$
\n" ); document.write( "(2) $\"+10u+%2B+t+=+2%2A%28+10t+%2B+u+%29+%2B+18+\"$
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\n" ); document.write( "(2) $\"+10u++%2B+t+=+20t+%2B+2u+%2B+18+\"$
\n" ); document.write( "(2) $\"+10u+-+2u+%2B+t+-+20t+=+18+\"$
\n" ); document.write( "(2) $\"+8u+-+19t+=+18+\"$
\n" ); document.write( "and, since
\n" ); document.write( "'(1) $\"+t+%2B+u+=+9+\"$
\n" ); document.write( "(1) $\"+u+=+9+-+t+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( "(2) $\"+8%2A%28+9+-+t+%29+-+19t+=+18+\"$
\n" ); document.write( "(2) $\"+72+-+8t+-+19t+=+18+\"$
\n" ); document.write( "(2) $\"+-27t+=+-54+\"$
\n" ); document.write( "(2) $\"+t+=+2+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+u+=+9+-+t+\"$
\n" ); document.write( "(1) $\"+u+=+7+\"$
\n" ); document.write( "The original number is 27
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\n" ); document.write( "check:
\n" ); document.write( "Reverse digits: $\"+72+\"$
\n" ); document.write( " $\"+72+=+2%2A%28+27+%29+%2B+18+\"$
\n" ); document.write( " $\"+72+=+54+%2B+18+\"$
\n" ); document.write( " $\"+72+=+72+\"$
\n" ); document.write( "OK\r
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