The problem describes a scenario where a principal is hosting a luncheon with a budget of $225. Each person gets two sandwiches, and sandwiches cost $3 each. At least 16 people are expected to attend. The goal is to identify the equations and inequalities that represent the constraints of this situation, where $n$ is the number of people attending and $s$ is the number of sandwiches.

1. Problem Description

The problem describes a scenario where a principal is hosting a luncheon with a budget of $

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5. Each person gets two sandwiches, and sandwiches cost $3 each. At least 16 people are expected to attend. The goal is to identify the equations and inequalities that represent the constraints of this situation, where $n$ is the number of people attending and $s$ is the number of sandwiches.

2. Solution Steps

Let's analyze each option:

A. $n \ge 16$: This inequality represents the fact that at least 16 people are attending, which is a constraint given in the problem.

B. $n \ge 32$: This is incorrect. The problem states that at least 16 people attend, not

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C. $s < 2n$: This is incorrect. Since each person gets two sandwiches, the number of sandwiches $s$ must be equal to $2n$, not less than $2n$.

D. $s = 2n$: This equation correctly represents the relationship between the number of people attending ($n$) and the number of sandwiches ($s$). Each person gets 2 sandwiches.

E. $3n \le 225$: This is incorrect. The total cost of sandwiches depends on the number of sandwiches, $s$, and each sandwich costs $

3. Since $s=2n$, the total cost is $3s = 3(2n) = 6n$. The budget is $225, so the inequality should be $6n \le 225$.

F. $3s \le 225$: This inequality represents the budget constraint. Since each sandwich costs $3, the total cost for$s$sandwiches is$3s$. The total cost must be less than or equal to the budget of$

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Therefore, the correct options are A, D, and F.

3. Final Answer

A. $n \ge 16$

D. $s = 2n$

F. $3s \le 225$