SOLUTION: 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 extrem

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?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the thousands digit
Let = the tens digit
Let = the units digit
The "value" of the number is:

------------------------------
(1)
(2)
(3)
------------------------------------------
There are 3 unknowns and 3 equations, so it's solvable
(1)
(1)
and
(2)
(2)
(2)
----------------
Add (3) and (2)
(3)
(2)
------------------

and, also:
(2)
Substitute the last results into (1)
(1)
(1)
(2)
(2)
(2)
(2)
and

and
(2)
(2)
(2)
-------------------
The original number is 153
------------------------
check:
(1)
(1)
(1)
(1)
-----------------------
(2)
(2)
(2)
-------------------------
(3)
(3)
(3)
OK
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