a skier is trying to decide whether or not to buy a season ski pass. a daily pass costs $350. the skier would have to rent skis with either pass for $25 per day. how many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?

Let's analyze the costs for both options:

1. **Daily Pass Option:**
   - Cost of a daily pass: $350 per day
   - Cost of renting skis: $25 per day
   - Total cost for $ x $ days: 
     \[
     \text{Total Cost} = 350x + 25x = 375x
     \]

2. **Season Pass Option:**
   - Cost of the season pass: $ P $ (we'll use $ P $ to represent the cost of the season pass)
   - Cost of renting skis: $25 per day
   - Total cost for $ x $ days:
     \[
     \text{Total Cost} = P + 25x
     \]

We need to find the number of days $ x $ where the season pass becomes less expensive than the daily passes. This occurs when the total cost of the season pass is less than the total cost of the daily passes:

\[
P + 25x < 375x
\]

To solve this inequality:

\[
P < 375x - 25x
\]
\[
P < 350x
\]
\[
x > \frac{P}{350}
\]

So, the skier would need to ski more than $ \frac{P}{350} $ days to make the season pass less expensive than purchasing daily passes.

If you have a specific price for the season pass $ P $, you can substitute it into the equation to find the exact number of days.

Would you like more details on this, or have any questions?

Here are 5 related questions for further exploration:
1. What happens if the daily rental cost changes to $30 per day?
2. How would the equation change if the skier got a discount on ski rentals with the season pass?
3. What if the skier plans to ski for only 10 days; is the season pass still a good deal?
4. How would you calculate the break-even point if the season pass also includes free ski rentals?
5. How would these calculations change if the skier is offered a multi-day pass at a discount?

**Tip:** Always check for discounts or additional perks included in a season pass to accurately assess its value against daily passes.

Explore the cost comparison between purchasing a season ski pass and daily ski passes with rental costs. Determine the break-even point and savings potential based on the number of skiing days. Suitable for high school students and skiers looking to optimize ski pass costs.

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