To find out how many batches of biscuits Sarah made, we first need to set up an equation based on the information provided.
Let \( x \) represent the number of batches Sarah made. Since each batch produces 75 biscuits, the number of biscuits from the batches would be \( 75x \).
According to the problem, Sarah also receives 60 biscuits from her friend. Therefore, the total number of biscuits Sarah ends up with is given by the equation:
\[ 75x + 60 = 360 \]
Now, let's solve for \( x \):
- Subtract 60 from both sides:
\[ 75x = 360 - 60 \] \[ 75x = 300 \]
- Now, divide both sides by 75:
\[ x = \frac{300}{75} \] \[ x = 4 \]
Thus, Sarah made 4 batches of biscuits.