Ciara is baking biscuits for a big sale. Each batch makes 75 biscuits and her friend gives her another 60 biscuits. She ends up with 360 biscuits total for the bake sale use algebra to solve for how many batches she made.

Let's assume the number of batches Ciara made is x.

So, the total number of biscuits Ciara made is 75x.
Her friend gives her another 60 biscuits, so the total number of biscuits becomes 75x + 60.
According to the information given, the total number of biscuits for the bake sale is 360 biscuits.
Therefore, the equation becomes:
75x + 60 = 360.
Simplifying the equation, we have:
75x = 360 - 60,
75x = 300.
Dividing both sides of the equation by 75, we get:
x = 300/75,
x = <<4=4>>4.
Therefore, Ciara made 4 batches of biscuits.