Mathematical Puzzles
Expert
2 min
A three-digit number has digits whose sum is 12. The hundreds digit is twice the tens digit, and the units digit is three more than the tens digit. What is the number?
Hint
Let the tens digit be x.
Answer
633.
Explanation
Let the tens digit be x. The hundreds digit is 2x and the units digit is x+3. Thus 2x+x+x+3=12, giving x=2.25, which is not an integer. Therefore no such three-digit number exists.
Step-by-Step Solution
Let tens digit = x.
Hundreds = 2x.
Units = x+3.
2x+x+x+3=12.
4x=9.
x=2.25.
A digit cannot be 2.25.
Therefore no valid number exists.
Hundreds = 2x.
Units = x+3.
2x+x+x+3=12.
4x=9.
x=2.25.
A digit cannot be 2.25.
Therefore no valid number exists.