A group of 6 friends are renting an airbnb. They’ll be staying for 2 nights 1 day. The total for all 3 days will be $334. 3 people will be staying for the full 2 nights. 3 people will only be staying 1 night. How will the cost be divided equally?

To divide the cost fairly between the 6 friends based on their stay duration, we need to establish a per-night cost and allocate the total cost proportionately to the amount of time each person stays.

### Step-by-step breakdown:

1. **Total cost**: \$334 for 3 days (2 nights and 1 day).
   
2. **Calculate the cost per night**:
   Since the focus is on the nights (since they affect how much each person stays), we divide the total cost by the 2 nights:
   \[
   \text{Cost per night} = \frac{334}{2} = 167
   \]
   So, each night costs \$167.

3. **Assign each person’s share**:
   - The **3 people staying for 2 nights** will pay for 2 nights each.
   - The **3 people staying for 1 night** will pay for just 1 night each.

4. **Calculate the total "person-nights"**:
   - The **3 people** staying 2 nights contribute a total of $3 \times 2 = 6$ "person-nights."
   - The **3 people** staying 1 night contribute a total of $3 \times 1 = 3$ "person-nights."
   
   Therefore, the total is $6 + 3 = 9$ "person-nights."

5. **Determine the cost per person-night**:
   Since the total cost is \$334 for 9 person-nights, the cost per person-night is:
   \[
   \text{Cost per person-night} = \frac{334}{9} \approx 37.11
   \]

6. **Calculate each group’s cost**:
   - Each of the **3 people staying for 2 nights** will pay for 2 person-nights:
     \[
     2 \times 37.11 = 74.22
     \]
   - Each of the **3 people staying for 1 night** will pay for 1 person-night:
     \[
     1 \times 37.11 = 37.11
     \]

### Final breakdown:
- **3 people staying for 2 nights**: Each pays \$74.22.
- **3 people staying for 1 night**: Each pays \$37.11.

Let me know if you'd like more details or if anything is unclear!

Here are 5 related questions:
1. How would the total cost change if they stayed for 3 nights instead?
2. What if the 3 people staying for 1 night had to cover the full day’s share as well?
3. How would the cost be divided if the rental had additional charges like cleaning or taxes?
4. What if one person stayed an extra night—how would the division change?
5. Could a different cost allocation method be fairer?

**Tip**: Always calculate per-night or per-person charges to fairly divide shared expenses, especially when people have varying levels of participation.

A group of 6 friends are renting an Airbnb. They’ll be staying for 2 nights and 1 day. The total for all 3 days will be $334. 3 people will be staying for the full 2 nights. 3 people will only be staying 1 night. How will the cost be divided equally?

Learn how to fairly divide an Airbnb rental cost of $334 for 6 friends staying for different durations. This problem involves calculating cost per night, proportional allocation, and determining each person's share. Perfect for students in Grades 6-8 looking to understand real-world math applications.

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