
Part 1 of 2

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Part 1

Jaylen will choose between two catering companies for an event. Company A charges a​ set-up fee of​ $500 plus​ $25 for each guest. Company B charges a​ set-up fee of​ $200 plus​ $30 per guest. Complete parts a and b.

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Part 1

**a.** Write expressions to determine the amount each company charges for g guests.

The expression to determine the amount Company A charges for g guests is 

enter your response here. 

The expression to determine the amount Company B charges for g guests is 

enter your response here. 

​(Type expressions using g as the variable. Do not include the​ $ symbol in your​ answer.)

The expression to determine the amount Company A charges for g guests is. The expression to determine the amount Company B charges for g guests isThe expression to determine the amount Company B charges for g guests is(Type expressions using g as the variable. Do not include the $ symbol in your answer.)

Let's solve the problem step by step.

### Part 1a: Write expressions to determine the amount each company charges for $ g $ guests.

#### Company A:
- **Set-up fee:** $500
- **Cost per guest:** $25

The total cost for Company A, for $ g $ guests, is the sum of the set-up fee and the cost per guest multiplied by the number of guests.

**Expression for Company A:**
\[
\text{Total cost for Company A} = 500 + 25g
\]

#### Company B:
- **Set-up fee:** $200
- **Cost per guest:** $30

The total cost for Company B, for $ g $ guests, is the sum of the set-up fee and the cost per guest multiplied by the number of guests.

**Expression for Company B:**
\[
\text{Total cost for Company B} = 200 + 30g
\]

### Summary of Expressions:
- **Company A:** $ 500 + 25g $
- **Company B:** $ 200 + 30g $

These are the expressions that represent the total charges for each company based on the number of guests, $ g $.

Do you have any questions or need further details on this part? 

Here are 5 related questions to consider:
1. How many guests would result in the same total cost for both companies?
2. What is the total cost for each company if there are 100 guests?
3. How does the cost difference between the two companies change as the number of guests increases?
4. For what range of guest numbers is Company A the cheaper option?
5. How would the expressions change if Company A reduced their set-up fee by $100?

**Tip:** When comparing costs from different companies, always identify the fixed and variable costs to understand how the total cost scales with quantity (in this case, the number of guests).

Learn how to calculate total costs for catering companies A and B based on the number of guests. This problem involves arithmetic calculations and linear equations. Suitable for students in Grades 7-9.

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