document.write( "Question 515818: The tens digit of a two digit number is 2 less than twice the ones digit. If the number is reversed, the new number is 18 less than the original number \n" ); document.write( "

Algebra.Com's Answer #344171 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = the tens digit
\n" ); document.write( "Let $\"b\"$ = the ones digit
\n" ); document.write( "given:
\n" ); document.write( " $\"+a+=+2b+-+2+\"$
\n" ); document.write( " $\"+a+=+2%2A%28+b-1%29+\"$
\n" ); document.write( " $\"+10a+%2B+b+\"$ is the original number
\n" ); document.write( " $\"+10b+%2B+a+\"$ is the reverse of the number
\n" ); document.write( " $\"+10b+%2B+a+=+10a+%2B+b+-+18+\"$
\n" ); document.write( " $\"+10%2A%28a-b%29+%2B+b-a+=+18+\"$
\n" ); document.write( " $\"+10%2A%28a-b%29+%2B+b-a+=+18+\"$
\n" ); document.write( " $\"+10a+-+10b+%2B+b+-+a+=+18+\"$
\n" ); document.write( " $\"+9a+-+9b+=+18+\"$
\n" ); document.write( " $\"+a+-+b+=+2+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+2%2A%28b-1%29+-+b+=+2+\"$
\n" ); document.write( " $\"+2b+-+2+-+b+=+2+\"$
\n" ); document.write( " $\"+b+=+4+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+a+=+2%2A%28+b-1%29+\"$
\n" ); document.write( " $\"+a+=+2%2A3+\"$
\n" ); document.write( " $\"+a+=+6+\"$
\n" ); document.write( "The original number is 64
\n" ); document.write( "check:
\n" ); document.write( "Reverse the digits: 46
\n" ); document.write( "64 = 46 + 18
\n" ); document.write( "OK \n" ); document.write( "

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