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Excel Can an array formula reliably do this kind of totaling?

I want to sum (by month) sales by person and multiply by the price to get total sales by month. I thought something like {=SUM(SUM(B5:E12)*G5:G12)} or just plain {=SUM(B5:E12)*G5:G12} would work, but it doesn't, as you can see in the cell identified as "Wrong". The cell marked "Right" is a simple sum of the extended products above it--I added the sales in weeks 1 thru 4 then multiplied the total by the price for each row. Is there an array formula or some other approach that won't involve extra/hidden row

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