An event planner is planning a party. It costs the event planner a onetime fee of

The correct answer is $25$. The total cost of the party is found by adding the onetime fee of the venue to the cost per attendee times the number of attendees. Let $x$ be the number of attendees. The expression $35+10.25x$ thus represents the total cost of the party. It's given that the budget is $\$300$, so this situation can be represented by the inequality $35+10.25x\le 300$. Subtracting $35$ from both sides of this inequality gives $10.25x\le 265$. Dividing both sides of this inequality by $10.25$ results in approximately $x\le 25.854$. Since the question is stated in terms of attendees, rounding $25.854$ down to the greatest whole number gives the greatest number of attendees possible, which is $25$.