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How to SUM the VLOOKUP results based on condition in other column using ARRAYFORMULA in google sheets?

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I would like to sum all the costs based on the products purchased between specific dates.

=SUM(ARRAYFORMULA(IFERROR(VLOOKUP('Purchased List Table'!B2:B,'Pricing Table'!A2:B,2,0),"")))

With the formula above, I managed to sum all the prices of all products in the Purchased List Table instead of a certain timeframe.

How could I modify the formula in order to sum only the costs of products within specific timeframe (e.g.: between 9/3/2021 to 9/5/2021 only)?

Thank you.


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