SOLUTION: The sum of the digits of a three -digit number is 17. The ones degit is two more than the hundreds digit. The tens digit is one more than the hundreds digit. What is the number?

Note: I changed your 17 in the first sentence to 18, because 
with 17, the digits come out with fractions, and digits cannot 
be fractions.

The sum of the digits of a three-digit number is 18. The ones 
digit is two more than the hundreds digit. The tens digit is 
one more than the hundreds digit. What is the number?

Let the leftmost digit be L  (that's called the "hundreds digit")
Let the middle digit be M    (that's called the "tens digit") 
Let the rightmost digit be R (that's called the "ones" digit)

>>...The sum of the digits of a three -digit number is 18...<<

That says:

L + M + R = 18 

>>...The ones digit is two more than the hundreds digit...<<

That says:

R = L + 2

>>...The tens digit is one more than the hundreds digit.,,<<

That says:

M = L + 1

So you have this syetem of equations:

L + M + R = 18
R = L + 2
M = L + 1

You might write the last two this way:

 L + M + R = 18
-L     + R =  2
-L + M     =  1

If you can't solve that system then post again.

Answer: L = 5, M = 6, R = 7 so the number is 567.

Edwin