the sum of the digit of a number consisting of three digits is 12 the middle digits is equal to half the sum of the other two if the order of the digits is reverse the number is diminished by 198 find the number.
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Answer: 543
Step-by-step explanation:
Let a be the hundreds digit, b be the tens digit and c be the ones digit
Then a+b+c=12
b=12-a-c -------(1)
b=(a+c)/2 --------(2)
100a+10b+c-198=100c+10b+a
99a-99c = 198
99(a-c) = 198
a-c = 2----(3)
From (1) and (2), 12-a-c=(a+c)/2
24-2a-2c=a+c
3a+3c=24
a+c=8-----(4)
(3) + (4) --->
2a = 10
a = 5
(4)-(3)
2c=6
c=3
From (2), b=(5+3)/2 = 4
The number is 543
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