SAT Question 74c98c82: Linear Inequalities answer and explanation with Desmos solution

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 $$200$, so this situation can be represented by the inequality $35+10.25x\le 200$. The greatest number of attendees can be found by solving this inequality for $x$. Subtracting $35$ from both sides of this inequality gives $10.25x\le 165$. Dividing both sides of this inequality by $10.25$ results in approximately $x\le 16.098$. Since the question is stated in terms of attendees, rounding $x$ down to the nearest whole number, $16$, gives the greatest number of attendees possible.