I'm looking for the syntax to multiply a column of Rates (eg A3:A5)
by the sums of selected values (eg C3:D5) in the row for each Rate.

A B C D E
1 Hrs Hrs Hrs Hrs
2 Rate Jan Feb Mar Apr
3 100 10 40 70 75
4 200 20 50 80 85
5 300 30 60 90 95

The result would equal A3*sum(C3:D3)+A4*sum(C4:D4)+A5*sum(C5:D5)

I know this can be done by using separate sum and sumproduct formulas,
but I'm looking for a single formula, since I need to use it in many instances in a very large spreadsheet.

The following attempt, of course, does not work:

=SUMPRODUCT(A3:A5,SUM(C3:D3):SUM(C5:D5))

Any assistance will be greatly appreciated.