I plan on cooking a prime rib for an upcoming dinner party for eight adults. I would like to have enough beef leftover to make a soup or stew. I plan on cooking the prime rib to medium rare. Is it best to calculate the amount by the number of bones per person or by pounds? How much prime rib should I purchase to feed my guests?
Prime rib is usually sold two ways, Bone-In or Bone-Out. For a Bone-In prime rib an 8 pound should serve you well, for a Bone-Out, Six will do nicely. I would also highly recommend you refer to the prime rib narrative of "Cooks Illustrated The New Best Recipe Book" to learn how to prepare your roast.
Most restaurants that I have either had or seen Prime Rib served at will offer 10 oz or 12 oz serving size, with some variations in the overall 8-16 oz (225g - 450g) range. Appetites will vary from person to person, and you may wish to not serve the 'heals' as they will be more well done than the center, though some guests may prefer this..so, 'your-mileage-may-vary'. The very size of beef ribs makes serving them 'bone-in' impractical, as it results in a serving that is too thick for a single serving (though some restaurants do this for eye-appeal). For your home dinner party I would not recommend planning based on 'bone count'. Even if you buy and cook your roast "bone-in" your first cut after preparing and resting the meat should be to remove the bones from the roast. Since leftovers are goal you have set for this preparation you may wish to then slice the roast "on the bias" (about a 15°-20° angle from perpendicular to the bone section) as it will produce a larger footprint on the plate. The ends will provide you with good meat to include in a soup or slice up for sandwiches.
7lb 3ribs roast should make for 6-8 servings.