document.write( "Question 1132364: A 3 digit number such that it is equal to 19 times the sum of its digit. What is the largest possible value? example 114 = 19 * (1+1+4) or 133 = 19 * (1+3+3) \n" ); document.write( "

Algebra.Com's Answer #749387 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Given the 3-digit number \"abc\", the value of the number is 100a+10b+c; the sum of the digits is a+b+c. So the statement of the problem says

\n" ); document.write( " $\"100a%2B10b%2Bc+=+19%28a%2Bb%2Bc%29\"$
\n" ); document.write( " $\"100a%2B10b%2Bc+=+19a%2B19b%2B19c\"$
\n" ); document.write( " $\"81a+=+9b%2B18c\"$
\n" ); document.write( " $\"9a+=+b%2B2c\"$

\n" ); document.write( "We want to find the largest 3-digit number that satisfies the condition of the problem.

\n" ); document.write( "To get the largest such number, we want the value of a to be as large as possible.

\n" ); document.write( "All three of a, b, and c have to be single digit integers.

\n" ); document.write( "In particular, the largest possible value for both b and c is 9.

\n" ); document.write( "So the largest possible value for a is found from

\n" ); document.write( " $\"9a+=+b%2B2c+=+9%2B2%289%29+=+27\"$
\n" ); document.write( " $\"a+=+3\"$

\n" ); document.write( "And so the largest 3-digit number that satisfies the conditions is with a = 3 and b = c = 9: 399.
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