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Does he go outside?
Is he using the bathroom that you know of for both peeing and pooping?
When he vomits, is it pretty much just the food he eats, or does he vomit on an empty stomach too?
Thank you for the extra information.
Occasional stomach upset is very common in cats. I just went through a bout myself with my 5yo male cat.
It could definitely be from hairball causing a problem. I would start giving him a dab of Vaseline daily. Just wipe a dab on his paw, and he should most likely lick it off himself. If he doesn't just try to quickly wipe it on the roof of his mouth.
lighten up his diet for a couple days. Use boiled chicken or beef with some rice, no seasoning. If that is too much trouble for you since you work long hours, just try baby food. This is very gentle on the stomach. Use any flavor you think he would like such as chicken or turkey. Make sure there are no onions or garlic in it including onion and garlic powder.
Also crush a 1/2 tablet of Pepcid AC in his food once daily. This does a GREAT job settling an upset stomach and reducing stomach acid, which is common in cats to have high stomach acid.
If the problem still continues after all this, then a vet check up is wise.