SOLUTION: there are three digits. the first digit is double the third digit, the second digit is prime and all digits add up to 9, what are all three digits

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Question 467447: there are three digits. the first digit is double the third digit, the second digit is prime and all digits add up to 9, what are all three digits
Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
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.