Final answer:
Assuming a 1:1 ratio for granola to peanuts, the greatest number of full batches of trail mix that can be made is 8 batches, as the ingredient with the lesser amount (peanuts) will run out after the 8th batch.
Step-by-step explanation:
To determine the greatest number of full batches of trail mix you can make with 12 cups of granola and 8 1/2 cups of peanuts, we first need to establish the ratio of granola to peanuts for a single batch of trail mix. Since the question does not provide this information, we will assume that the ratio is 1:1, meaning that we need equal amounts of granola and peanuts for one batch of trail mix. Therefore, the number of full batches will be limited by the ingredient with the lesser amount.
We have 8 1/2 cups of peanuts, which is the lesser amount compared to the 12 cups of granola. Since we assume a 1:1 ratio for granola and peanuts in one batch, we can only make 8 1/2 batches because we would run out of peanuts at that point. However, we cannot make half of a batch, so we must round down to the nearest whole number. This means that the greatest number of full batches of trail mix we can make is 8 batches.