1995 Saturn SL1 Low oil

I have a problem with this car burning oil. As a result I have to add a quart every 2k miles otherwise the engine will make a ticking noise.
My mother drove the car for 2 days with it making the noise intermittently. The oil light flickered on and went off, never coming back on again.
I've since replaced the lost oil and ran the car in the drive way. Its still making the ticking noise.
My question is how bad is this? Can it be repaired and preferably at a low cost?