document.write( "Question 809000: The sum of the digits of a three digit number is 11. The hundreds digit exceeds the sum of the tens digit and the units digit by 1. When the digits are reversed, the new numbers is 396 less than the original number. Find the number. \n" ); document.write( "

Algebra.Com's Answer #487338 by lwsshak3(11628) $\"\"$ $\"About$

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The sum of the digits of a three digit number is 11. The hundreds digit exceeds the sum of the tens digit and the units digit by 1. When the digits are reversed, the new numbers is 396 less than the original number. Find the number.
\n" ); document.write( "***
\n" ); document.write( "let u=units digit
\n" ); document.write( "let t=tens digit
\n" ); document.write( "let h=hundreds digit
\n" ); document.write( "...
\n" ); document.write( "u+t+h=11
\n" ); document.write( "h=u+t+1
\n" ); document.write( "..
\n" ); document.write( "100h+10t+u=100u+10t+h+396
\n" ); document.write( "...
\n" ); document.write( "u+t+h=11
\n" ); document.write( "u+t-h=-1
\n" ); document.write( "subtract
\n" ); document.write( "2h=12
\n" ); document.write( "h=6
\n" ); document.write( "..
\n" ); document.write( "u+t-h=-1
\n" ); document.write( "u+t-6=-1
\n" ); document.write( "u+t=5
\n" ); document.write( "t=5-u
\n" ); document.write( "..
\n" ); document.write( "100h+10t+u=100u+10t+h+396
\n" ); document.write( "100*6+10t+u=100u+10t+6+396
\n" ); document.write( "10t cancels out
\n" ); document.write( "600+u=100u+6+396
\n" ); document.write( "99u=198
\n" ); document.write( "u=2
\n" ); document.write( "t=5-u=3
\n" ); document.write( "original number:632 \n" ); document.write( "

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