FLAGSTAFF, Ariz. — Tourists returned to the Grand Canyon on Saturday after Arizona officials along with several counterparts agreed to a federal government plan to reopen national parks, which had been closed as a result of the partial government shutdown.

But the Obama administration’s OK to reopen tourist areas across the nation came with a big caveat: States must foot the bill with money they likely won’t see again.

So far, Utah, Colorado, South Dakota, Arizona and New York have agreed to open parks that had been closed since the beginning of the month. Meanwhile, governors in other states were trying to gauge what would be the bigger economic hit – paying to keep the areas operating or losing the tourist money that flows when the scenic attractions are open.

South Dakota and several corporate donors worked out a deal with the National Park Service to reopen Mount Rushmore beginning Monday. Republican Gov. Dennis Daugaard said it will cost $15,200 a day to pay the federal government to run the landmark in the Black Hills. He said he has wired four days’ worth of donations.

In New York, Democratic Gov. Andrew Cuomo said his state will pay $61,600 a day to fully fund Park Service personnel and the Statue of Liberty will open Sunday.