nformation about the costs of three catering companies is shown in this table. Gavin can spend no more than $300 on the catering for an event. What is the greatest number of people that Gavin can have at his event without spending more than $300 on catering?
Acme Catering Company
Best Foods Company
Creative Catering Company
$6 per person plus a flat $100 service charge
$8 per person plus a flat $40 service charge
$10 per person with no service charge
A.
30
B.
32
C.
33
D.
37

To determine the greatest number of people Gavin can invite while staying within the $300 budget, we need to calculate the total cost for each catering company and compare the results. Here's how we do it:

### 1. **Acme Catering Company**
   - Cost per person: $6
   - Service charge: $100
   - Total cost equation: $ \text{Total Cost} = 6n + 100 $
   - Set this equation less than or equal to $300: 
     \[
     6n + 100 \leq 300
     \]
   - Subtract $100 from both sides:
     \[
     6n \leq 200
     \]
   - Divide by 6:
     \[
     n \leq \frac{200}{6} \approx 33.33
     \]
   - Maximum number of people: $ n = 33 $

### 2. **Best Foods Company**
   - Cost per person: $8
   - Service charge: $40
   - Total cost equation: $ \text{Total Cost} = 8n + 40 $
   - Set this equation less than or equal to $300:
     \[
     8n + 40 \leq 300
     \]
   - Subtract $40 from both sides:
     \[
     8n \leq 260
     \]
   - Divide by 8:
     \[
     n \leq \frac{260}{8} = 32.5
     \]
   - Maximum number of people: $ n = 32 $

### 3. **Creative Catering Company**
   - Cost per person: $10
   - Service charge: $0
   - Total cost equation: $ \text{Total Cost} = 10n $
   - Set this equation less than or equal to $300:
     \[
     10n \leq 300
     \]
   - Divide by 10:
     \[
     n \leq \frac{300}{10} = 30
     \]
   - Maximum number of people: $ n = 30 $

### Conclusion
The greatest number of people Gavin can invite without exceeding $300 is **33** people with **Acme Catering Company**. 

Thus, the correct answer is:

**C. 33**

Would you like more details or have any questions?

Here are five related questions for further practice:

1. How would the maximum number of people change if the budget was increased to $350?
2. What if the service charge for Best Foods Company was $50 instead of $40?
3. How does the maximum number of people compare if the cost per person at Creative Catering is reduced to $9?
4. What is the total cost for each company if Gavin invites 25 people?
5. If Gavin wants to invite 35 people, which company would exceed the budget and by how much?

**Tip:** When dealing with budget constraints, always start by solving the equation for the maximum number of units you can afford before comparing different options.

Discover how to maximize event attendance within a $300 budget using different catering costs. Solve the problem step-by-step with formulas and inequalities for Acme Catering, Best Foods Company, and Creative Catering. Suitable for Grades 7-9.

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