Rogar is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine the number of package of hot dogs Roger must buy?

Options

A. `(p)/(8)ge78`
B. `8pge78`
C. `8+pge78`
D. `78-pge8`

Answer

To determine the number of packages of hot dogs Roger must buy for his picnic, we can set up an inequality based on the information provided.

1. **Identify the total number of guests**: Roger has 78 guests.

2. **Determine how many hot dogs are needed**: Since Roger plans to serve each guest at least one hot dog, he needs at least 78 hot dogs.

3. **Understand the packaging**: Each package of hot dogs contains 8 hot dogs. If we let \( p \) represent the number of packages, then the total number of hot dogs Roger has can be expressed as \( 8p \).

4. **Set up the inequality**: Since Roger needs at least 78 hot dogs, we can write the inequality:
\[ 8p \geq 78 \]

5. **Conclusion**: The inequality \( 8p \geq 78 \) represents the relationship between the number of packages of hot dogs \( p \) and the total number of hot dogs needed for the guests.

### Final Answer:
The inequality that could be used to determine the number of packages of hot dogs Roger must buy is:
\[ 8p \geq 78 \]