im not an expert or anything, but i think for the innequality, i would say
[tex]6.50p + 100 \leqslant 500[/tex]
as far as the amount of people she can invite, do 500-100=400 because of the setup fee, then, to find how many people she can invite. 400Ă·6.50 which leaves you with the highest amount of people she can invite without going over budget, as 61.