It is given that

$$Costofcake=\mathrm{\$}35$$

$$Cateringexpensesperperson=\mathrm{\$}15$$

Then

$$TotalCost=\mathrm{\$}35+\mathrm{\$}15p$$

As they will spend at most $\mathrm{\$}300$ for his party, the total cost should be less than or equal to $\mathrm{\$}300$.

$$\therefore \mathrm{\$}35+\mathrm{\$}15p\le 300$$

So choice K is correct.