Let \( x \) represent the number of batches Siara made. Each batch makes 75 biscuits, so the total number of biscuits from the batches is \( 75x \).
According to the problem, her friend gave her an additional 60 biscuits, and the total number of biscuits she ends up with is 360.
We can set up the equation:
\[ 75x + 60 = 360 \]
Now, we will solve for \( x \).
First, subtract 60 from both sides of the equation:
\[ 75x = 360 - 60 \]
\[ 75x = 300 \]
Next, divide both sides by 75:
\[ x = \frac{300}{75} \]
\[ x = 4 \]
Therefore, Siara made 4 batches of biscuits.