put (something) at
To set, determine, or estimate the value or price of something. Just by looking at the condition of the item, I'd put the value of your antique at around $2,300, though of course this could change significantly at auction. That extra night in the hotel puts your bill at $450.
put (something) at (some amount of money)
To estimate that something will cost a certain amount of money, especially when that figure is particularly large. The mechanic put the repairs at nearly $700 between parts and labor. Early reports are putting the company's newest smartphone at nearly $1,000.
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