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Algebra / Linear inequalities in one or two variables Difficulty: Medium

An event planner is planning a party. It costs the event planner a onetime fee of $dollar sign 35$ to rent the venue and $dollar sign 10.25$ per attendee. The event planner has a budget of $dollar sign 200$ . What is the greatest number of attendees possible without exceeding the budget?

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Explanation

The correct answer is $16$ . 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 $35 plus 10.25 x$ thus represents the total cost of the party. It's given that the budget is $dollar sign 200$ , so this situation can be represented by the inequality $35 + 10.25 x \leq 200$ . The greatest number of attendees can be found by solving this inequality for $x$ . Subtracting $35$ from both sides of this inequality gives $10.25 x less than or equals 165$ . Dividing both sides of this inequality by $10.25$ results in approximately $x less than or equals 16.098$ . 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.