Why does pressure stay the same when partition between equal gas volumes is removed?

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Homework Statement



An isolated container is divided into two equal volumes by partition. In each part of the container there is an ideal gas. They have the same pressure P. The partition is removed. Which of the following is the final pressure:
A: P/2
B:P
C:3P/2
D:2P

Homework Equations


PV=nRT (I assume)

The Attempt at a Solution



Well, I know the right answer is B, the answer key says so, but I am not sure why. I thought about using this equation PV/T = constant, therefore T = PV, and P=T/V, so if volume is doubled, and T is constant, then P will be halved. I am not sure if this is right. Any help? :)
 
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The partial pressure of both gases will be P/2 but the partial pressures add up, resulting in P.

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