After you remove the stem from the valve body---look inside the open hole where the stem goes-----all the way in the back ,you will see the opening that your rubber washer will touch when the stem is installed---
That is the 'seat'---they get pitted and coroded after years of use.
You can remove and replace that 'seat' --most use a long Allen wrench and simply unscrew----
If you have a plumbing supply house near by, you might get better advice and the right parts.---The Depot may have a few valve seats---but a supply house will be a better bet---Mike----
PS--rebuild the hot and cold while you are at it----and ask for a roll of 'valve stem packing' while you are at the store.
These two pics should show you what Mike is describing.
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