Lawn Tractor Engine Problems

I have a 1995 Craftsman lawn tractor with the two-cylinder 18.5 horsepower engine. Last weekend, it started without a problem but after about 15 minutes or so of mowing it began to sputter and backfire through the muffler. Fortunately, I was just finishing up at the time but I planned to check the engine before the next mowing.
Well, I didn't and the same thing happened yesterday; ran fine for a while then started the sputtering. This morning I adjusted the carb screws per the manual but when I turned it on, it ran very fast and wouldn't slow to a reasonable idle speed. I turned down the fast fuel mixture screw a bit, which helped. I did a bit more mowing but this time it began sputtering very quickly.
I had pulled the plugs before starting and they looked good, no noticeable difference between the two. The intake manifold seems tight, as do the bolts holding the carb to the manifold. Any ideas on why it starts acting up at full operating temperature?
Paul
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Pavel314 wrote:

Pull the air cleaner and inspect it. While you've got it off, check the choke plate to make sure it's wide open when the choke lever is "off".
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