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

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Accepted Answer

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 + 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 ≤ 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 ≤ 165. Dividing both sides of this inequality by 10.25 results in approximately x ≤ 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.

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