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Default Combine SUMIF and SUMPRODUCT

Here is how the data is setup:

A B C
Type Qt. Rate
Category1 5 $10.00
Category2 6 $2.00
Category1 .5 $.50
Category2 10 $7.00

Here is the objective:

Calculate total amount, by mulitplying Qt. and Rate, if Category = category1
SUMPRODUCT doesn't take an argument for condition, and SUMIF can't multiply.
Is there a formula that combines them both?
 
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