A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $66. 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 assume the skier goes skiing for x number of days.
The cost of renting skis for x days would be 20*x = $<<20*x=20x>>20x.
The cost of using daily passes for x days would be 66*x = $<<66*x=66x>>66x.
To make the season pass less expensive than the daily passes, we set up the following inequality:
400 + 20x < 66x
Subtracting 20x from both sides, we get:
400 < 46x
Dividing both sides by 46, we get:
400/46 < x
Approximately, 8.6957 < x
Therefore, the skier would have to go skiing for more than 8.6957 or 9 days in order to make the season pass less expensive than the daily passes.
To determine how many days the skier would have to go skiing in order to make the season pass less expensive than the daily passes, we need to compare the costs of both options.
The cost of a daily pass is $66, and the skier would also have to rent skis for $20 per day. Therefore, the total cost of a day of skiing with a daily pass would be $66 + $20 = $86.
On the other hand, the cost of a season pass is $400, and the skier would still have to pay for rentals at $20 per day.
Let's calculate the breaking point - the number of days the skier would have to go skiing to make the season pass less expensive than the daily passes:
$400 (Season pass cost) = $86 (Daily pass cost per day) * X (Number of days)
Dividing both sides by $86:
$400 / $86 = X
X ≈ 4.65 (rounded to two decimal places)
So, the skier would have to go skiing for approximately 4.65 days (or 5 days) to make the season pass less expensive than purchasing daily passes.
To determine how many days the skier would have to go skiing in order to make the season pass less expensive than the daily passes, we need to compare the total costs for both options.
Let's define the variables:
- D = cost of a daily pass ($66)
- S = cost of a season pass ($400)
- R = cost of renting skis per day ($20)
- n = number of days the skier would have to go skiing
For the daily pass option, the cost per day would be calculated as: D + R. So, the total cost for n days would be n * (D + R).
For the season pass option, the skier only needs to pay the cost of renting skis once. Therefore, the total cost for n days would be S + n * R.
To make the season pass less expensive than the daily passes, we need to set up an inequality:
S + n * R < n * (D + R)
Substituting the given values, we have:
400 + n * 20 < n * (66 + 20)
Simplifying the inequality:
400 + 20n < 66n + 20n
400 < 86n
Dividing both sides by 86:
400/86 < n
4.65 < n
Therefore, the skier would have to go skiing for at least 5 days to make the season pass less expensive than the daily passes.