SAT Question b78cd5df: 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 $$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 $25$.