Question 1183763: A three-digit number whose hundreds digit is twice the tens digit and the tens digit is 3 more that
the units digit
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the 3 digit number is HTU
H is the hundreds digit
T is the tens digit
U is the units digit.
each digit can be 0 through 9.
if the hundreds digit is 2 times the tens digit, then the tens digit can't be 5 or greater because then the hundreds digit will be two digits.
therefore, the tens digits can only be 0 or 1 or 2 or 3 or 4.
of the tens digit is 3 more than the units digit, then the units digit has to be 3 less than the tens digit.
since the units digit can't be less than 0, then the tens digit can only be 3 or 4.
if the tens digit is 3, then the hundreds digit is 6 and the units digit is 0 and the number is 630.
this satisfies the requirements since the hundreds digit is two times the tens digit and the tens digit is 3 more than the units digit.
if the tens digit is 4, then the hundreds digit is 8 and the units digit is 1 and the number is 841.
this satisfies the requirements since the hundreds digit is two times the tens digit and the tens digit is 3 more than the units digit.
630 and 841 are the only two possibilities as far as i can see.
if you say that the digit can't be 0, then the only possible number is 841.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
A three-digit number whose hundreds digit is twice the tens digit and the tens digit is 3 more that
the units digit
Let units digits be U
Then tens digit = U + 3, and hundreds digit is: 2T, or 2(U + 3) = 2U + 6
By observation, with the hundreds digit being 2U + 6, U or the units digit CANNOT be 2 or more.
Therefore, U or the units digit MUST either be 0 or 1.
First case: Units digit = 0
Tens digit = 0 + 3 = 3
Hundreds digit = 2(0) + 6 = 6
Number, based on the above: 
Second case: Units digit = 1
Tens digit = 1 + 3 = 4
Hundreds digit = 2(1) + 6 = 8
Number, based on the above: 
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