document.write( "Question 1037159: there is a certain number consisting of 3 digits which is equal to17th times the sum of the digits and if 198 be added to the number, the digits will be reversed also sum of extreme digits is less than the middle digits by 1 find original number? \n" ); document.write( "

Algebra.Com's Answer #651886 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+h+\"$ = the thousands digit
\n" ); document.write( "Let $\"+t+\"$ = the tens digit
\n" ); document.write( "Let $\"+u+\"$ = the units digit
\n" ); document.write( "The \"value\" of the number is:
\n" ); document.write( " $\"+100h+%2B+10t+%2B+u+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "(1) $\"+100h+%2B+10t+%2B+u+=+17%2A%28+h+%2B+t+%2B+u+%29+\"$
\n" ); document.write( "(2) $\"+100h+%2B+10t+%2B+u+%2B+198+=+100u+%2B+10t+%2B+h+\"$
\n" ); document.write( "(3) $\"+h+%2B+u+=+t+-+1+\"$
\n" ); document.write( "------------------------------------------
\n" ); document.write( "There are 3 unknowns and 3 equations, so it's solvable
\n" ); document.write( "(1) $\"+100h+%2B+10t+%2B+u+=+17h+%2B+17t+%2B+17u+\"$
\n" ); document.write( "(1) $\"+83h+=+7t+%2B+16u++\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+99h+-+99u+=+-198+\"$
\n" ); document.write( "(2) $\"+99u+-+99h+=+198+\"$
\n" ); document.write( "(2) $\"+u+-+h+=+2+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Add (3) and (2)
\n" ); document.write( "(3) $\"+u+%2B+h+=+t+-+1+\"$
\n" ); document.write( "(2) $\"+u+-+h+=+2+\"$
\n" ); document.write( "------------------
\n" ); document.write( " $\"+2u+=+t+%2B+1+\"$
\n" ); document.write( " $\"+t+=+2u+-+1+\"$
\n" ); document.write( "and, also:
\n" ); document.write( "(2) $\"+h+=+u+-+2+\"$
\n" ); document.write( "Substitute the last results into (1)
\n" ); document.write( "(1) $\"+83h+=+7t+%2B+16u++\"$
\n" ); document.write( "(1) $\"+83%2A%28+u-2+%29+=+7%2A%28+2u+-+1%29+%2B+16u++\"$
\n" ); document.write( "(2) $\"+83u+-+166+=+14u+-+7+%2B+16u+\"$
\n" ); document.write( "(2) $\"+83u+-+166+=+30u+-+7+\"$
\n" ); document.write( "(2) $\"+53u+=+159+\"$
\n" ); document.write( "(2) $\"+u+=+3+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+t+=+2u+-+1+\"$
\n" ); document.write( " $\"+t+=+2%2A3+-+1+\"$
\n" ); document.write( " $\"+t+=+6+-+1+\"$
\n" ); document.write( " $\"+t+=+5+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+h+=+u+-+2+\"$
\n" ); document.write( "(2) $\"+h+=+3+-+2+\"$
\n" ); document.write( "(2) $\"+h+=+1+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "The original number is 153
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+100h+%2B+10t+%2B+u+=+17%2A%28+h+%2B+t+%2B+u+%29+\"$
\n" ); document.write( "(1) $\"+100%2A1+%2B+10%2A5+%2B+3+=+17%2A%28+1+%2B+5+%2B+3+%29+\"$
\n" ); document.write( "(1) $\"+153+=+17%2A9+\"$
\n" ); document.write( "(1) $\"+153+=+153+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "(2) $\"+100h+%2B+10t+%2B+u+%2B+198+=+100u+%2B+10t+%2B+h+\"$
\n" ); document.write( "(2) $\"+153+%2B+198+=+351+\"$
\n" ); document.write( "(2) $\"+351+=+351+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(3) $\"+h+%2B+u+=+t+-+1+\"$
\n" ); document.write( "(3) $\"+1+%2B+3+=+5+-+1+\"$
\n" ); document.write( "(3) $\"+4+=+4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );