Rim problem..

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I'm putting a like-new S-7 rear rim with a coaster brake on my bike; and I ran into a problem: The chain is way too loose. After a quick count of the teeth on the cog/gear in both the old rim and the new one; it appears that the S-7's cog has fewer teeth.

My question is... can I just swap the gears? They're both coaster brake models, and look pretty much identical.

Since it possibly makes a difference; the S-7 came off a Fair Lady (I think) and the old S-2 came off a Sting-Ray.

I just want to make sure before I tear it apart...
 
Yeah, its almost too easy.......I swap rear cogs around quite a bit to get the final ratio I want for the intended use; ie, a park bike vs a road bike or biketrail bike. A 44 or 46 front with a 19 rear is a common, and easy to pedal ratio, a 16 rear gets tough on hills. If Im tired or lazy the 16 is my top edge, and too much if I have a hill and headwind. I just changed a 46/16 to a 46/17 and am liking it.
 
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