It is not clear how C
a and C
i relate to 24% and 34%.
In general your equation
Ci*Vi + Ca*Va = Cf*(Vi+Va)
is reasonably OK, but it ignores fact volumes are (in general) not additive (V
f is not guaranteed to be equal to sum of V
i and V
a). Masses are additive though, which makes the problem solvable with the help of the density table.
Depending on how accurate result you need this approach can be good enough though.
If you need really accurate result try to download the
concentration calculator - it does exact calculations for mixing (if memory serves me well density table for nitric acid is built in). Free trial version should be enough for you to check if the numbers are OK.
I can help with the program if something is not clear.