Dennis and Nancy are celebrating their 30th wedding anniversary. We’re having a reception at Tiffany Oak reception hall the $3000 for the reception of the reception hall charge a $50 cleanup fee plus $34 per person the number of people that they may still stay within their budget, making an inequality to solve this.

Answer 1

Let's define some variables to represent the situation:

• Let \( p \) be the number of people attending the reception.
• The total cost for the reception can be expressed as follows:

1. The base fee for the reception hall is $3000.
2. There is a cleanup fee of $50.
3. The cost per person is $34.

Thus, the total cost \( C \) can be calculated with the following equation:

\[ C = 3000 + 50 + 34p \] This simplifies to:

\[ C = 3050 + 34p \]

Next, we need to assign a maximum budget for Dennis and Nancy. Let's denote their budget as \( B \). Assuming their budget is just for the purpose of this problem (since it's not provided), we can set it let's say at $5000 for the sake of this inequality (adjust this value as necessary based on the actual budget).

We want to ensure that the total cost does not exceed their budget, so we can set up the inequality like this:

\[ 3050 + 34p \leq 5000 \]

Now, let's solve the inequality for \( p \):

1. Subtract 3050 from both sides:

\[ 34p \leq 5000 - 3050 \] \[ 34p \leq 1950 \]

2. Divide both sides by 34:

\[ p \leq \frac{1950}{34} \] \[ p \leq 57.35 \]

Since the number of people must be a whole number, we round down to the nearest whole number:

\[ p \leq 57 \]

Therefore, Dennis and Nancy can invite up to 57 people while staying within their budget of $5000. If their actual budget is different, you can adjust the initial value in the inequality accordingly.