Final answer:
To find out how many batches were made, divide 1 barrel by 3/8 to get 8/3 or 2 and 2/3 batches. Since partial batches aren't practical, the factory made 2 full batches of granola bars.
Step-by-step explanation:
The question asks us to determine how many batches of granola bars were made by a factory, given that it uses 3/8 of a barrel of raisins in each batch and used up a whole barrel yesterday. To find out how many batches were made, we can divide the total amount of raisins used by the amount used per batch.
Let's assign the total amount of a barrel of raisins used by the factory as 1 (since they used up the entire barrel) and divide it by the fraction representing the amount used per batch, which is 3/8:
Total batches = Total amount used / Amount per batch = 1 / (3/8)
To divide by a fraction, we multiply by its reciprocal. So, we multiply by 8/3:
Total batches = 1 × (8/3) = 8/3
Therefore, the factory made 8/3 batches of granola bars yesterday, which is equivalent to 2 and 2/3 batches. Since we can't have a fraction of a batch in practical terms, the answer is C. 2 full batches with some leftover raisins that were not enough to complete another whole batch.