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The problem asks to find expressions for the cost charged by two companies based on the number of guests, $ g $.

Here’s how we can break it down:

- **Company A** charges:
  - A set-up fee of \$500
  - Plus \$25 per guest.

  The total cost for $ g $ guests will be:
  \[
  500 + 25g
  \]

- **Company B** charges:
  - A set-up fee of \$200
  - Plus \$30 per guest.

  The total cost for $ g $ guests will be:
  \[
  200 + 30g
  \]

### Answers:
- Expression for Company A: $ 500 + 25g $
- Expression for Company B: $ 200 + 30g $

Would you like help with the next part or any further explanations?

Here are 5 related questions you can consider:
1. How many guests would make Company A and Company B charge the same amount?
2. If Jaylen expects 100 guests, which company would be cheaper?
3. What is the minimum number of guests where Company B becomes more expensive than Company A?
4. If Company A increased its set-up fee to \$600, how would that affect the expression?
5. What would the cost be for 50 guests with each company?

**Tip:** Whenever you have a problem involving fixed costs and variable costs, you can always express it as a linear equation!

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

Explore how to compare the costs between two catering companies using algebraic expressions. Company A charges $500 plus $25 per guest, while Company B charges $200 plus $30 per guest. Learn how to write linear expressions for each company's charges, suitable for students in Grades 6-8.

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