document.write( "Question 1118053: A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number. Show solution \n" ); document.write( "

Algebra.Com's Answer #733276 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "When a 2-digit number is reversed and the difference between the original number and the new number is calculated, it is always 9 times the difference between the two digits:

\n" ); document.write( " $\"%2810t%2Bu%29-%2810u%2Bt%29+=+10t%2Bu-10u-t+=+9t-9u+=+9%28t-u%29\"$

\n" ); document.write( "So in your problem, since the difference between the two numbers is 9, you know that the tens digit is 1 more than the units digit:
\n" ); document.write( " $\"t+=+u%2B1%29\"$

\n" ); document.write( "If an algebraic solution is required, then you can use that equation along with the one that says the number is 1 more than 6 times the sum of its digits to finish the problem:

\n" ); document.write( " $\"t+=+u%2B1\"$ ; $\"10t%2Bu+=+6%28t%2Bu%29%2B1\"$

\n" ); document.write( "Or if you aren't required to show an algebraic solution, then simply look at all the 2-digit numbers that have the tens digit 1 more than the units digit and find the one for which the number is 1 more than 6 times the sum of its digits. \n" ); document.write( "

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