I'm confused about mathematical expression concerning Boyle's Law. Can you help me out?

I’m refreshing my physics and came in contact with a symbol I haven’t seen before.

For Boyle’s law, it can be written a few ways.

In the book I’m using, which is a navy publication, it simplified Boyle’s Law as VP=V’P’

I wasn’t sure what the ’ was, so I looked it up and it said:

“In physics, the prime is used to denote variables after an event. For example, VA′ would indicate the velocity of object A after an event.”

But I’m still not grasping the concept.

Here’s an example of Boyle’s Law from the book:

V= initial volume
P= inital pressure
V’= new volume
P’= new pressure

20cm3 of gas a has a pressure of 1,000 hPa. The pressure is increased to 1,015 hPa. What is the new volume?

So, 20 x P = V’ x P’

20×1000 = V’ x 1015

20,000 = V’ x 1015

So V’ = 20,000/1015 which is 19.70cm3

My question is: where did the division come from? I get the rest, and the division makes sense, but I don’t understand why I’m supposed to divide. Does it have something to do with the prime (’)?

Other examples show Boyle’s Law as pV=k and P1V1 = P2V2

And why is it pressure to volume for one and volume to pressure on another?