My in laws have very little water pressure in the house an a pressure tank from 1972 has a valve stem on top and only 15lb on that.

Two types of pressure tanks. If the tank has a valve stem it is what is known as a bladder tank. Bladder tanks are usually painted. Non-bladder tanks are galvanized, do not have a valve stem and are referred to as a pressure tanks.

Bladder tanks last until the bladder leaks or ruptures or until the tank itself begins to leak. Galvanized pressure tanks last until they begin to leak.

Water pressure is determined by the pump settings. Bladder tanks have to be pre-charged with air. The air pressure, with the pump off and the tank drained, should be 2 lbs. less than the cut on pressure of the pump switch setting.

Sound like a bladder tank to me. Let's check it out. With the pump up to pressure and shut off pop the snifter valve on top of the tank. If water comes out then the bladder is ruptured and the tank must be replaced. It's just air comes out then shut the pump off and open a cold water tap to bleed off to pressure. Now, charge that tank with two PS I under the cut in point of the control box.
What does a pressure gauge read when the tank shuts off? Back to you, Tom