Question 467447
Let's call the first digit x, the second digit y, and the third digit z. 

We know that the digits add up to 9, so x + y + z = 9. 

We also know that the first digit is double the third digit, so x = 2*z. Plugging this into the above gives 

2z + y + z = 9 
3z + y = 9 
y = 9 - 3z 

We also know that z cannot be larger than 3 (otherwise y would be negative). 

Can z be equal to 3? No, because y = 0 is not prime. 
Can z be equal to 2? Yes, because y = 3 is prime. 
Can z be equal to 1? No, because y = 6 is not prime. 
Can z be equal to 0? No, because y = 9 is not prime. 

Therefore, the second digit is y=3, the third digit is z=2, and the first digit is x = 2*z = 2*2 = 4. 

Now we can check. Note that the digits add up to 9 since  x + y + z = 4+3+2 = 9. The first digit (4) is double the third digit (2), and the second digit (3) is prime.