Trudy's Radio Repair

Trudy's Radio Repair is an unmarked quest

Detailed walkthrough
First of all, speak to Trudy, and ask her about the group of people who shot you. She will explain that they came into the bar a lot, and also knocked over her radio, breaking it. Ask to fix the radio, and she will let you, explaining how she'll pay you for the work. Go behind the counter of the Prospector Saloon, and activate the radio. With a Repair skill of 20, you can fix it. Otherwise, a Fixin' Things skill magazine can be used to raise your Repair skill, if needed; one can be found on the bookshelf next to the pool table. If you're able to repair it, report back to Trudy. She will then reward you with 50 caps. If you can pass a Barter check (20 Barter), she will pay you an extra 25 caps. You will gain 10 XP for fixing it, but an extra 25 XP if you pass this check.

Bugs
If Trudy is not spoken to before finishing "They Went That-a-Way", she will not display the proper dialogue option to initiate the quest.