The corporate team-building event will cost $2,310 if it has 77 attendees. How many attendees can there be, at most, if the budget for the corporate team-building event is $2,850? Assume the relationship is directly proportional.


Since the relationship between the cost and the number of attendees is directly proportional, we can set up a proportion to solve the problem.

Given:
- The event costs $2,310 for 77 attendees.
- We need to find the maximum number of attendees $x$ that can be accommodated with a budget of $2,850.

The proportion is:

\[
\frac{\text{cost}}{\text{attendees}} = \frac{\text{cost}}{\text{attendees}}
\]

\[
\frac{2310}{77} = \frac{2850}{x}
\]

To solve for $x$, cross-multiply:

\[
2310 \times x = 2850 \times 77
\]

\[
2310x = 219450
\]

Now, divide both sides by 2310:

\[
x = \frac{219450}{2310} \approx 95
\]

So, the event can have a maximum of **95 attendees** within the budget of $2,850.

Would you like to see a detailed explanation or have any further questions?

Here are some related questions:
1. What is the cost per attendee for the corporate event?
2. If the budget were $3,000, how many attendees could be accommodated?
3. How much would the event cost if there were 100 attendees?
4. How many attendees could be accommodated with a budget of $2,000?
5. What would the total cost be for 150 attendees?
6. If the cost per attendee decreases, how will it affect the maximum number of attendees?
7. How does the number of attendees change if the budget increases by 10%?
8. If there were a fixed cost added to the event, how would that affect the number of attendees?

**Tip:** When dealing with proportional relationships, you can easily scale quantities up or down by using the ratio between the known quantities.

Learn how to maximize the number of attendees for a corporate team-building event within a budget of $2,850. Understand the direct proportional relationship between cost and attendees. Suitable for middle school students studying proportional relationships.

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