Here is a very interesting system of equations which is rather intriguing to solve.
We begin with this setup, which is actually a mechanism to measure a volume of air. The capacity of the large container on the left is being measured. Say, for example, it is being used by Joanne the scientist. She pulls the handle of the pneumatic cylinder on the bottom to use the system. This pulls the two connected plungers in the middle, compressing the air in the container. Depending on the size of the container, pressure increases at a different rate. Once it is high enough, the horses are balanced and the plungers come to a stop. From how much they lowered, the volume is determined. A rather efficient mechanism, requiring only that the container be airtight and very little material. There is one small problem. How can the capacity possibly be calculated? For a start to this challenge, the supplementary air tank is half a litre, neglect air in the tubing, and let the amount pulled be 50 mL. Create a formula to find the capacity of the container given the volume by which the cylinder is displaced; the volume that was pulled out of it. Perhaps go further and find a general formula.