Sum with multiple criteria and vlookup from another table

In the table below, I want to sum all of New York ACT in Q2 after the sales have been multiplied by the corresponding rates. Is there a one-shot formula I can use without needing to multiply all the items of the first table with the corresponding rates, then summing? The result I'm looking for would be (49*.45)+(10*.37)=25.45.

table image here