Engagement Photo Shoot - Out of State

Hi there! We're getting married in a different state than where we currently live and the photographer I hired had said he'd be willing to travel to our city for our engagement shoot as long as we covered his travel and a hotel room for one night. I was willing to do that, but then he asked for a set amount that is much higher than I expected and don't think it's a fair cost. From my research, a nice hotel and a plane or train ticket would be much less. It feels that he would be making additional profit (significant profit) on that cost. I'm trying to figure out how to handle it and am curious others' thoughts if you've had a photographer travel for your engagement shoot. Is it normal to just pay one set cost or should I ask for travel/hotel receipts to pay for those? If the former, is it fair to offer a lower amount with research?