im not an expert or anything, but i think for the innequality, i would say
![6.50p + 100 \leqslant 500](https://img.qammunity.org/2019/formulas/mathematics/middle-school/lby0guky0c5u7rjpo07kuowkg65k5oenzz.png)
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. 400÷6.50 which leaves you with the highest amount of people she can invite without going over budget, as 61.