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Trader Joe's doesn't really do traditional sales or coupons, so your best bet there is just knowing which items are consistently cheap (their store brand stuff, seasonal produce). Whole Foods has better discounts if you're a Prime member - you get instant markdowns on a bunch of items every week, plus digital coupons through their app. Hitting up the clearance section near closing time can score you deals on stuff that's about to expire, and both stores mark down meat and prepared foods pretty aggressively toward the end of the day.
Don't wait for big sales events at either place - they're not built that way. I shop at both pretty regularly and honestly the real move is just sticking with their house brands and whatever's on the markdown shelf (Whole Foods especially has a whole section of stuff they're trying to move). At Whole Foods the Prime membership does add up over time with their digital deals, but at Trader Joe's you're basically paying the same price whether you shop today or next month, so just grab what's there.
If you're expecting doorbusters or weekly circulars like a typical grocery chain, you're setting yourself up for frustration at both places. The real gotcha that people miss is that Whole Foods Prime discounts only hit certain items each week - you have to actually open the app or check their site to see which ones, because walking in blind hoping for deals is a waste of time. Your loyalty card (or Prime membership for WF) matters way more than hunting for sales, and honestly the cheapest move at either store is just building your shopping list around whatever's already marked down that particular week rather than deciding what you want first and hoping it's on sale.
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