SOLUTION: The hundred's digit of of a number of three figures is 1/2 of the ten's digit and is less than the unit's digit by 3. If the number be divided by the sum of its digits, the quotien

Question 340849: The hundred's digit of of a number of three figures is 1/2 of the ten's digit and is less than the unit's digit by 3. If the number be divided by the sum of its digits, the quotient is 22.Find the number.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
There seems to be something wrong but here goes:
Let x=hundred's digit
Then 2x=ten's digit
And x+3=unit's digit
Sum of the number's digits:x+2x+x+3=4x+3
So our equation to solve is:
(100x+20x+x+3)/(4x+3)=22 multiply each side by 4x+3 and simplify
121x+3=88x+66 subtract 88x and 3 from each side
121x-88x+3-3=88x-88x+66-3 collect like terms
33x=63
x=1.909 which rounds off to 2
so x=2
2x=4
x+3=5
The number is 245
ck
245/11=22.2 which rounds off to 22
Another way to look at this problem:
Clearly the 100's digit cannot be greater than 4. If it was, then the 10's digit would itself be a 2-digit number which is not allowed
So we only have 4 possibilities for the 100's digit:
if the 100's digit is 1
the 10's digit is 2 and the unit's digit is 4
the number would be 124
if the 100's digit is 2
the 10's digit is 4 and the units digit is 5
the number would be 245
if the 100's digit is 3
the 10's digit is 6 and the unit's digit is 6
the number would be 366
if the 100's digit is 4
the 10's digit is 8 and the unit's digit is 7
the number would be 487
The number 245, although not an exact solution, comes closer than any of the others
Hope this helps---ptaylor
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