Here's a chart indicating tire sizes for certain wheel widths.

Tire Width for a Wheel/Rim Size Chart

If your F has 20" wheels you have 20x9 in the front and 20x10.5 in the rear.

 

245/40 would be the throw-away tire size to use for both front and rear 19" wheels. Fairly easy tire size to find under $125.

 

Yikes, now y'all have me wanting to check my tires, lug nuts, alignment...

I was thinking about the diff too, that would be a good solution, UNLESS it was an AWD, then all four have to be exactly the same, right? I have a friend that fried her diff on an AWD Volvo wagon. Not because of different sizes, just because she got two new tires and had two worn tires...

 

Naw, nothing to worry about. The car with the three 17s and one 18 was an AWD Volvo VR. The one that upset me was the MB Wagon when they put on the wrong load rating (not XL) and then under inflated it.

 

Oh, that's interesting, my friend's totally fried.
But dang, makes you wonder about these people...