Welcome to the Forum!
We are here, in part, to help new folks avoid newbie mistakes. Goat has given you excellent advise I will not repeat. He is exactly correct.
Trailer salesmen will say anything to make a sale. Most truck salesman are not up to speed on trailer towing weight calculations. Advertising folks use strange math. Read the fine print.
Manufacturers may CLAIM this FW is ? ton towable because the bare naked nothing on board dry wt is only 7845# and the pin wt IN THIS CONDITION is only 1550#. Many (but certainly not all) ? ton pickups have a payload greater than 1550#. With their logic, that makes it ? ton towable.
The TRUTH is even empty, you need a 200# hitch to tow it, and the weight of all passengers must be included, as well as all the other stuff goat correctly listed. Load up a family of 4 (600#) plus the hitch and pin wt, and we are already at 2350#. My guess is less than 10% of all ? ton trucks have a payload over 2350#.
If you want to do it safely and within manufacturer's weight limits, follow Goat's advise.
All is not lost. A FW places 20% of its' weight squarely in the bed of the truck. A TT places only 10% of its' weight on the tongue. Assuming a 1800# payload and 800# of people, pets and other cargo in the truck, the biggest FW you could handle is one with a 800# pin wt or a 4000# FW. 800# pin, 200# hitch, 800# people & cargo = 1800# payload. By comparison, that same truck and family could handle a 9,000# TT. 900# tongue wt, 80# WD hitch, 800# people & cargo = 1780#.