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I couldn't find the max. towing capacity in the '77 brochure, but the max. GVWR is 10,000# for the reg. cab F-350 dual Cab/Chassis. Crew cab version is the same, but Super cab is 9,250#
Ive looked in my Owners Manual. It says for the 137'' WB F-350 w/ dual wheels is 9,500lbs, but that's with a 351 V8. 161'' WB F-350 w/ dual wheels is 10,000lbs, but again with a 351 V8. Id swap out that 300 I6 to atleast a 400 if your going to do some towing.
Look at the vin tag on your door, your GVW will be listed there. Take the running weight of your truck. Include fuel, passengers, dog, tires and luggage. subtract running weight from GVW and you will have your max tongue weight and then you will know how heavy a trailer you can Legally pull.