If you buy travel online, either on an airline website or one of the many online travel agencies such as Expedia and Priceline, you've probably seen what looks like a dubious pitch: "Book air and hotel together and save (fill in X amount of dollars)."
It takes some extra digging to see if the savings are real, but usually packages do indeed cost less than booking airfare and hotel separately. To prove that packages save money, you need to visit the airline's website, find a fare for your dates of travel, and then move over to the hotel's website to see what their lowest price is, then add the two amounts and compare the combined price to what the online travel agency would charge for a package on the same flights and the same room types.
Recently, I was booking a trip from New York to Detroit and did the math. On bookingbuddy.com I discovered that were I to buy a hotel plus air package my airfare on American Airlines would be thrown in for free. So I did some random searches on other itineraries and found that the deal was not a fluke.
Here are three recent examples I found: