Brad is taking his family on a vacation to the mountains, and he is deciding on a cabin to rent. The cabins at Rainbow Peak cost $104 per night, plus a one-time fee of $43 for service and cleaning. The cabins at Verdant Meadows cost $66 per night, plus a one-time fee of $195.
Which equation can you use to find n, the number of nights the vacation would need to last for the two cabins to cost the same?

To find the number of nights, $ n $, for which the total cost of staying at Rainbow Peak and Verdant Meadows would be the same, we can set up an equation based on the total cost formulas for each cabin.

1. **Cost at Rainbow Peak**: 
   - The cost per night is $104.
   - The one-time fee is $43.
   - The total cost after $ n $ nights is:
   \[
   \text{Total cost at Rainbow Peak} = 104n + 43
   \]

2. **Cost at Verdant Meadows**:
   - The cost per night is $66.
   - The one-time fee is $195.
   - The total cost after $ n $ nights is:
   \[
   \text{Total cost at Verdant Meadows} = 66n + 195
   \]

To find when the costs are the same, set the two total cost expressions equal to each other:
\[
104n + 43 = 66n + 195
\]

This equation can be solved for $ n $ to find the number of nights for which the total cost will be the same at both locations.

Would you like me to solve this equation step-by-step?

Here are 5 related questions:
1. What is the total cost of staying 5 nights at Rainbow Peak?
2. How much would Brad pay at Verdant Meadows for 3 nights?
3. If Brad stays for 7 nights at Rainbow Peak, how much more would he pay compared to Verdant Meadows?
4. For how many nights does Rainbow Peak become more expensive than Verdant Meadows?
5. If Brad has a budget of $800, how many nights can he afford at Rainbow Peak?

**Tip**: When dealing with linear equations involving real-world problems, always set up cost expressions clearly for comparison.

Brad is taking his family on a vacation to the mountains, and he is deciding on a cabin to rent. The cabins at Rainbow Peak cost $104 per night, plus a one-time fee of $43 for service and cleaning. The cabins at Verdant Meadows cost $66 per night, plus a one-time fee of $195. Which equation can you use to find n, the number of nights the vacation would need to last for the two cabins to cost the same?

Solve the linear equation to find how many nights Brad needs to stay for the total costs at Rainbow Peak and Verdant Meadows to be the same. Learn the cost formulas and compare options with this step-by-step guide. Ideal for students in Grades 6-8.

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