2 columns of values, summing values in column 1 if corresponding number in column 2..

Hi,

If I have 2 columns of numbers, and I want to sum the number in column 1 if the numbers in column 2 meet a certain criteria.

So, say I have $ amounts in Column A. I want to sum the $ amounts where the corresponding numbers in column B are >0 and <30.

So
Column A Column B
5 20
10 50
2 0
4 5

Thus, the formula should add 5+4 = 9 automatically

Any help is very much appreciated! Thanks!