Let \( x \) be the number of batches Siara made. Each batch makes 75 biscuits, so the total number of biscuits from the batches is \( 75x \). She receives an additional 60 biscuits from her friend, and the total number of biscuits she ends up with is 360.
We can set up the equation as follows:
\[ 75x + 60 = 360 \]
Now, we will solve for \( x \):
- Subtract 60 from both sides:
\[ 75x = 360 - 60 \] \[ 75x = 300 \]
- Divide both sides by 75:
\[ x = \frac{300}{75} \] \[ x = 4 \]
Therefore, Siara made 4 batches of biscuits.