a skier is trying to decide whether or not to buy a season ski pass. a daily pass costs $62. a season ski pass costs $400. the skier would have to rent skis with either pass for $20 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 calculate the number of days the skier would need to ski to make the season pass less expensive than the daily passes.

1. **Daily Pass Option:**
   - Cost of a daily pass: $62 per day
   - Cost of renting skis: $20 per day
   - Total cost for $ x $ days:
     \[
     \text{Total Cost} = (62x + 20x) = 82x
     \]

2. **Season Pass Option:**
   - Cost of the season pass: $400
   - Cost of renting skis: $20 per day
   - Total cost for $ x $ days:
     \[
     \text{Total Cost} = 400 + 20x
     \]

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

\[
400 + 20x < 82x
\]

To solve this inequality:

\[
400 < 82x - 20x
\]
\[
400 < 62x
\]
\[
x > \frac{400}{62} \approx 6.45
\]

Since the number of days must be a whole number, the skier would need to ski at least **7 days** for the season pass to be less expensive than buying daily passes.

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

Here are 5 related questions for further exploration:
1. How would the break-even point change if the season pass were priced at $500?
2. What if the ski rental cost increased to $30 per day?
3. How many days would make the daily pass more economical if the skier only skis occasionally?
4. What if there were a multi-day discount for daily passes?
5. How would different pricing strategies for ski rentals affect the decision?

**Tip:** Always round up when calculating the break-even point for situations like these, as partial days are not usually feasible.

Learn how to calculate ski pass costs to decide between daily and season passes. Understand the cost differences based on daily pass price, season pass price, and ski rental costs. Suitable for Grades 6-8.

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