document.write( "Question 164607: Find a three digit number whose tens digit is 4 times the hundred’s digit and the unit’s digit is one more than the ten’s digit. The square of the sum of the digits is 72 more than the number? \n" ); document.write( "

Algebra.Com's Answer #121287 by vleith(2983) $\"\"$ $\"About$

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Let H be the hundred digit.
\n" ); document.write( "Then the tens digit is 4H
\n" ); document.write( "The ones digit is 4H+1\r
\n" ); document.write( "\n" ); document.write( "The \"number is (H*100)+(4H*10)+(4H+1) = (100H)+(40H)+(4H+1)= 144H + 1
\n" ); document.write( "The sum of the digits is H+4H+4H+1 = 9H+1\r
\n" ); document.write( "\n" ); document.write( "You are told the square of the sum of the digits is 72 more than the number itself
\n" ); document.write( "So
\n" ); document.write( " $\"%289H%2B1%29%5E2+-+72+=+144H+%2B+1\"$
\n" ); document.write( " $\"81H%5E2+%2B+18H+-71+=+144H+%2B+1\"$
\n" ); document.write( " $\"81H%5E2+-126H+-+72+=+0\"$ }
\n" ); document.write( " $\"%289H+%2B+4%29%289H+-+18%29+=+0+\"$
\n" ); document.write( "H = -4/9 or 18/9=2
\n" ); document.write( "Since the number is an integer, the answer must be H=4\r
\n" ); document.write( "\n" ); document.write( "Test your answer. Does $\"289+=+19%5E2+-+72+\"$ \n" ); document.write( "

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