It is not possible. There are six cases:

1. a < b < c

2. a < c < b

3. b < a < c

4. b < c < a

5. c < a < b

6. c < b < a

Now, no expression containing a is ever less than anything, so I zeroed in on cases 4 and 6. The following assignments satisfy all inequalities:

Case 4. a = 5, c = 2, b = 1

Case 6. a = 5, c = 1, b = 1.5

Therefore, you cannot deduce the correct ordering. My observation that no expression containing a is ever less than anything is, I think, part of the reason you can't make the deduction.