Using the sample data you provided- headers in row 1 from column A ~ I
and the criterion and data in A2:I13, I got a solution by adding two
elements. The first is a total column, J, that sums your data in
advance. The next is a max age number in cell B13: it was easier to
add the max age of 999 rather than figure out a solution that left that
cell blank. By using 999 you are effectively providing an unlimited
ceiling age, but still one the formula logic can work with.

If you'll enter your target age in cell A16, enter this formula in B16:
=SUMPRODUCT(--(A16=$A$2:$A$13),--(A16<=$B$2:$B$13),$J$2:$J$13)

The formula checks your indicated age to see where it fits in the grid,
and returns the total from column J.