document.write( "Question 1082461: A number is 7 times the sum of its digits. If the digits are reversed, the new number is 30 less than twice the original. \n" ); document.write( "

Algebra.Com's Answer #696526 by Fombitz(32388) $\"\"$ $\"About$

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A and B are integers from 0-9.
\n" ); document.write( "Let the original number be $\"10A%2BB\"$ .
\n" ); document.write( "The sum of its digits would be $\"A%2BB\"$ .
\n" ); document.write( "Digits reversed would be $\"10B%2BA\"$ .
\n" ); document.write( "So,
\n" ); document.write( " $\"10A%2BB=7%28A%2BB%29\"$
\n" ); document.write( " $\"10A%2BB=7A%2B7B\"$
\n" ); document.write( " $\"3A=6B\"$
\n" ); document.write( "1. $\"A=2B\"$
\n" ); document.write( "and
\n" ); document.write( " $\"10B%2BA=2%2810A%2BB%29-30\"$
\n" ); document.write( " $\"10B%2BA=20A%2B2B-30\"$
\n" ); document.write( "2. $\"19A-8B=30\"$
\n" ); document.write( "Substituting from 1 into 2,
\n" ); document.write( " $\"19%282B%29-8B=30\"$
\n" ); document.write( " $\"38B-8B=30\"$
\n" ); document.write( " $\"30B=30\"$
\n" ); document.write( "Solve for B, then use either equation to solve for A.\r
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