The <em>correct answer</em> is:
4 full batches.
Explanation:
To solve this, we need to see how many "servings" (the amount needed for the recipe) of granola and peanuts we have.
We have 12 cups of granola. We need 2 3/4 cups. We need to see how many 2 3/4 cup-sized "servings" there are in 12 cups. We do this by dividing:
12 ÷ 2 3/4
Write both of these as improper fractions:
12/1 ÷ 11/4
To divide fractions, flip the second one and multiply:
12/1 × 4/11 = 48/11 = 4 4/11
This means we have 4 full servings of granola.
We have 8 1/2 cups of peanuts. We need 1 1/3 cups. We need to see how many 1 1/3 cups-sized "servings" there are in 8 1/2 cups. We do this by dividing:
8 1/2 ÷ 1 1/3
We need to write both of these as improper fractions:
17/2 ÷ 4/3
To divide fractions, flip the second one and multiply:
17/2 × 3/4 = 51/8 = 6 3/8
We have 6 full servings of peanuts.
The greatest number of full batches we can make will be the smaller of the two full servings we have. We have 4 full servings of granola and 6 full servings of peanuts; we cannot make 6 full batches of trail mix, since we don't have enough granola. This means we can only make 4 full batches.
