To determine how many batches the chef made using a total of 16 cups of apples and blackberries, we should follow these steps:
1. Identify the amount of each fruit used per batch:
- Apples used per batch: 3 cups
- Blackberries used per batch: 1 cup
2. Calculate the total cups of apples and blackberries used per batch:
Since each batch uses 3 cups of apples and 1 cup of blackberries, we add these amounts:
[tex]\[
3 \text{ cups (apples)} + 1 \text{ cup (blackberries)} = 4 \text{ cups (total per batch)}
\][/tex]
3. Determine the total number of batches that use 16 cups of apples and blackberries:
Given the total amount of cups of apples and blackberries used is 16, and each batch uses 4 cups, we can find the number of batches by dividing the total cups by the cups used per batch:
[tex]\[
\frac{16 \text{ cups}}{4 \text{ cups per batch}} = 4 \text{ batches}
\][/tex]
Thus, the chef made 4 batches of the recipe.
So, the correct answer is:
[tex]\[
\boxed{4 \text{ batches}}
\][/tex]
