Help with what is probably an easy question please. Pressure Problem

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A tire is filled with air at 15 C and is at a gauge pressure of 220 kPa. If the air temperature goes to 46 C, what fraction of the original air must be released to maintain the original pressure?

Here is what I did:

15 + 273 = 288
46 + 273 = 319

PV = nRT

P1V1 = (n1)288

P2V2 = (n2)319

(n1)288 = (n2)319

(n1) * 288/319 = (n2)

288/319 = .90 so (n2) is 90 percent of (n1), and 10 percent should be removed.

Does this look right?

Thanks Very Much!
 

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That all looks right to me. The only assumption we need to make for your method to be correct is that the volume of the tires does not change, which seems reasonable.
 
Thanks very much LeonhardEuler!

This is for class, and I still have time, so if anyone else can see a problem with it, please let me know.

Thank you.
 
Just to add one thing... is the method of keeping n in the equation as I did correct?

Thanks again.