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After the Apocalypse

Puzzle 3: Getting Fuel

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To protect your tribe from the radioactive fallout that comes with the nightly storms, huge air-filtering machines are employed. Unfortunately, these machines take a very particular fuel which is hard to come by. This fuel contains cerium (Ce) and meitnerium (Mt)in an exact ratio of 16:9. It may also contain some amount of nitrogen (N), which is inert, and doesn't effect the quality of the fuel; however, if the ratio of cerium to meitnerium is off at all, the air-filtering machines will jam up and be completely useless.

Unfortunately, you don't have any means to directly measure the ratio of cerium to meitnerium. However, you do have a a cerinitrometer, which measures the ratio of cerium and nitrogen, and a nitmeitnerometer, which measures the ratio of nitrogen and meitnerium. Can you find the fuel you need?

Before you are 4 containers with about 40 liters of liquid each. You discover the only elements in each container are cerium, meitnerium, and nitrogen, so one of containers may contain usable fuel. Furthermore:
- Container A has a Ce:N ratio of 2:3 and a N:Mt ratio of 2:3
- Container B has a Ce:N ratio of 2:3 and a N:Mt ratio of 3:2
- Container C has a Ce:N ratio of 4:3 and a N:Mt ratio of 4:3
- Container D has a Ce:N ratio of 4:3 and a N:Mt ratio of 3:4
Which container holds usable fuel?
Container A
Container B
Container C
Container D
Later that day, you find a container holding 54 liters of what looks like fuel. Your instruments tell you that the only elements in this container are cerium, meitnerium, and nitrogen, and that the Ce:N ratio is 2:1 and the N:Mt ratio is 2:3. Nearby is a 20-liter container of pure cerium.
How much cerium should you add to the mixture to turn it into usable fuel?
liters
That evening, just as you are about to head back to camp, you find two 40-liter containers. Both contain only cerium, meitnerium, and nitrogen. The first holds 18 liters with a Ce:N ratio of 2:1 and a N:Mt ratio of 2:3. The second is completely full, with a Ce:N ratio of 4:3 and a N:Mt ratio of 2:1.
How much should you pour from the second container into the first in order to create usable fuel?
liters

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