Question 745477: six times the middle of a three digit number is the sum of the other two. if the number is divided by the sum of the digits, the answer is 51 and the remainder is 11 . if the digits are reversed, the number becomes smaller by 198 . find the number.
Found 2 solutions by savvyhush23, MathTherapy:
Answer by savvyhush23(50)   (Show Source):
You can put this solution on YOUR website! Ok, I didn't expect the number to be whole integer, my reason is the remainder 11.
Anyway, let,
h - hundreds place
t - tens place
u - unit place
The number is: 100h + 10t + u
Writing the equations:
Six times the middle of a three digit number is the sum of the other two:
the middle digit is t so,
1)
If the number is divided by the sum of the digits, the answer is 51 and the remainder is 11:
2) 
If the digits are reversed, the number becomes smaller by 198:
3) 
Note: see the interchanging of h and u in the equation (reversing the number)
simplifying 2): (4)
simplifying 3): (5)
substitute 1) to (4): (6)
Solve (5) and (6);
substitute value of h and u to (1)
therefore, h = 7.5261, t = 2.175 and u = 5.5261
Finally the number is: 100h + 10t + u = 779.886
Checking:
If the number is divided by the sum of the digits, the answer is 51 and the remainder is 11:
If the digits are reversed, the number becomes smaller by 198:
lets just take the whole number: 977 - 779 = 198
Answer by MathTherapy(10553)  (Show Source):
You can put this solution on YOUR website!
six times the middle of a three digit number is the sum of the other two. if the number is divided by the sum of the digits, the answer is 51 and the remainder is 11 . if the digits are reversed, the number becomes smaller by 198 . find the number.
The original number is: 
You can do the check!!
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