document.write( "Question 571992: A 2 digit number exceeds twice the sum of its digits by 9, that number when reversed gives 8 times the sum of its digits. Find the number \n" ); document.write( "

Algebra.Com's Answer #368258 by josmiceli(19441) $\"\"$ $\"About$

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Let the 10's digit = $\"+a+\"$
\n" ); document.write( "Let the 1's digit = $\"+b+\"$
\n" ); document.write( "The number is $\"+10a+%2B+b+\"$
\n" ); document.write( "The number reversed is $\"+10b+%2B+a+\"$
\n" ); document.write( "--------------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+10a+%2B+b+=+2%2A%28+a+%2B+b+%29+%2B+9+\"$
\n" ); document.write( "(2) $\"+10b+%2B+a+=+8%2A%28+a+%2B+b+%29+\"$
\n" ); document.write( "--------------------------------------
\n" ); document.write( "(1) $\"+10a+%2B+b+=+2a+%2B+2b+%2B+9+\"$
\n" ); document.write( "(1) $\"+10a+-+2a+%2B+b+-+2b+=+9+\"$
\n" ); document.write( "(1) $\"+8a+-+b+=+9+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+10b+%2B+a+=+8%2A%28+a+%2B+b+%29+\"$
\n" ); document.write( "(2) $\"+10b+%2B+a+=+8a+%2B+8b+\"$
\n" ); document.write( "(2) $\"+7a+=+2b+\"$
\n" ); document.write( "(2) $\"+a+=+%282%2F7%29%2Ab+\"$
\n" ); document.write( "Substitute this into (1)
\n" ); document.write( "(1) $\"+8a+-+b+=+9+\"$
\n" ); document.write( "(1) $\"+8%2A%282%2F7%29%2Ab+-+b+=+9+\"$
\n" ); document.write( "(1) $\"+16b+-+7b+=+63+\"$
\n" ); document.write( "(1) $\"+9b+=+63+\"$
\n" ); document.write( "(1) $\"+b+=+7+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+a+=+%282%2F7%29%2Ab+\"$
\n" ); document.write( "(2) $\"+a+=+%282%2F7%29%2A7+\"$
\n" ); document.write( "(2) $\"+a+=+2+\"$
\n" ); document.write( "The number is 27
\n" ); document.write( "check:
\n" ); document.write( " $\"+27+=+2%2A%28+2+%2B+7+%29+%2B+9+\"$
\n" ); document.write( " $\"+27+=+18+%2B+9+\"$
\n" ); document.write( " $\"+27+=+27+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+72+=+8%2A%28+2+%2B+7+%29+\"$
\n" ); document.write( " $\"+72+=+72+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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