You are a department head planning a team-building lunch with a budget of $500. The cost for each employee is $42.75. To find the maximum number of employees, $p$, who can attend without exceeding the budget, you use the inequality ${}42.75p \leq 500$ and find that $p \leq 11.69$. Based on the strategy for budget limits, what is the maximum number of employees you can invite?

Arrange the steps in the correct order for determining the maximum number of attendees for a corporate event with a fixed budget of $500 and a cost of ${}42.75 per person.

In the budget inequality ${}42.75p \leq 500$ used for event planning, match each algebraic component with the real-world value or constraint it represents.

True or False: When solving a budget limit inequality for the number of people ($p$) attending an event, if the calculation results in $p \leq 11.69$, you should round the final answer up to 12 because 11.69 is mathematically closer to 12 than to 11.

Interpreting Decimal Results in Event Budgeting

When solving a budget limit inequality to plan a company training event, such as ${}42.75p \leq 500$, the algebraic solution might result in a decimal like $p \leq 11.69$. Because the number of attendees must be a whole person and the total cost cannot exceed the strict budget limit, you must always round this decimal ____ to determine the maximum number of people allowed to attend.

Algebraic Budgeting Strategy for Corporate Events