I am a three digit number. My tens digit is double my units digit. The sum of my digits is 18. What number am I?

Question

I need the answer to this question to be played out with the working out

Answer 1

Here is another trial and error way to solve this:

 

Let abc be the 3 digit number.

 

a + b + c = 18

b = 2c

a + 2c + c = 18

 

a = 18 - 3c

 

Treat c as an independent variable, and generate a table of a, b, and c values with the 3 values being integers and ranging from 1 to 9.  You will find that only 2 lines in table meet all of these conditions:

 

c a b

____

 

3 9 6 ⇒ the number is abc = 963

4 6 8 ⇒ the number is abc = 684

 

(The other lines in the table have either a 0 or a 10 somewhere.) 

 

Note that 963 and 684 are the same numbers that Tony J. obtained.  

 

Answer 2

We can just try different values for the units digit until we find something that works:

 

1: Then our number is X21, which is impossible, because that can't add up to 18.

 

2: Then our number is X42. Again, impossible.

 

3: Our number is X63. This would work if X=9, and the number is 963.

 

4: Our number is X84. This would work if X=6, and the number is 684.

 

5: This is impossible, because the double of 5 is more than one-digit long. Nothing greater than 5 will work for the same reason.

 

The given number could either be 963, or else 684.