Acorporateteam-buildingeventcosts$ 8,plusanadditional$ 6perattendee.Howmanyattendeescantherebe,atmost,ifthebudgetforthecorporateteam-buildingeventis$ 50?

1. Break Down the Problem

To determine the maximum number of attendees for the corporate team-building event given the budget, we need to find how the total cost can be expressed in relation to the budget.

• Fixed cost for the event: $8
• Variable cost per attendee: $6
• Total budget: $50

2. Relevant Concepts

The total cost $C$ can be expressed as: $C = \text{Fixed Cost} + (\text{Cost per Attendee} \times \text{Number of Attendees})$ Where:

• Fixed Cost = $8
• Cost per Attendee = $6
• Number of Attendees = $n$

Thus, we can express the total cost as: $C = 8 + 6n$

3. Analysis and Detail

We need to find the maximum number of attendees $n$ such that the total cost does not exceed the budget of $50: $8 + 6n \leq 50$

Rearranging the inequality: $6n \leq 50 - 8$ $6n \leq 42$ $n \leq \frac{42}{6}$ $n \leq 7$

4. Verify and Summarize

To verify, let's calculate the total cost for 7 attendees: $C = 8 + 6 \times 7 = 8 + 42 = 50$ This matches the budget exactly, confirming that the calculation is correct.

Final Answer

The maximum number of attendees for the corporate team-building event is $n = 7$.