Estimating the abundance of type-Ia supernovae using magnitude limited survey I would like to estimate the fraction of type-Ia supernovae in a magnitude limited survey (only including those supernovae that are brighter than a certain than a given fixed apparent magnitude). 

I currently have the following information:


Type-Ia supernovae are usually around 2.5 magnitudes brighter than core-collapse supernovae.
Volume limited surveys found that 30% of supernovae within a fixed distance from us are type-Ia. 


How can I solve this problem using the above information? The formula for apparent magnitude $m = -2.512\log_{10}(d/10\mathrm{pc})+c$ seems like an obvious starting point, but doesn't seem to lead anywhere. A worked solution would be very helpful.
The rudiments of a solution would be take your apparent magnitude limit and work out how far away you can see type Ia supernovae and how far away you can see core collapse supernovae.

Within the latter distance, 30% of the supernovae would be type Ia. Beyond that distance, all of the observed supernovae would be type Ia.

You then need to be assuming something about the density of supernova progenitors and thinking about any spread in their absolute magnitudes. And you didn't mention any observational uncertainties.