A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $67. 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 that the skier goes skiing for x number of days.
The cost of renting skis for x days with a daily pass would be 20x dollars.
So the total cost with a daily pass would be 67x + 20x = 87x dollars.
The cost of the season pass is 400 dollars.
The season pass would be less expensive than the daily passes if:
400 < 87x
Dividing both sides of the inequality by 87:
400/87 < x
Approximately:
4.6 < x
So the skier would have to go skiing for at least 5 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 total cost of using the daily pass with renting skis versus the cost of using the season pass with rental skis.
Let's start by calculating the total cost of using the daily pass for a certain number of days:
Total cost of using daily pass = (Daily pass cost + Skis rental cost) x Number of days
Therefore, the total cost of using the daily pass for a certain number of days can be expressed as:
Total cost of using daily pass = ($67 + $20) x Number of days
Total cost of using daily pass = $87 x Number of days
On the other hand, the total cost of using the season pass with rental skis can be expressed as:
Total cost of using season pass = Season pass cost + (Skis rental cost x Number of days)
Therefore, the total cost of using the season pass with rental skis can be expressed as:
Total cost of using season pass = $400 + ($20 x Number of days)
Total cost of using season pass = $400 + $20 x Number of days
Now, we need to find the number of days where the total cost of using the season pass becomes less than the total cost of using the daily pass.
Mathematically, this can be represented as:
Total cost of using season pass < Total cost of using daily pass
$400 + $20 x Number of days < $87 x Number of days
Simplifying this inequality:
$400 < ($87 - $20) x Number of days
$400 < $67 x Number of days
Now, divide both sides of the inequality by $67 to solve for the number of days:
$400 / $67 < Number of days
5.97 < Number of days
As the number of days must be a whole number, we can conclude that the skier would have to go skiing for at least 6 days in order to make the season pass less expensive than the daily passes.
To determine if the season ski pass is less expensive than the daily passes, we need to compare the total cost of skiing with each option.
Let's start by calculating the total cost of skiing with daily passes.
Each daily pass costs $67, and renting skis for each day costs an additional $20. So, the total cost per day with a daily pass is $67 + $20 = $87.
Now, let's calculate the total cost of skiing with the season ski pass.
The season ski pass costs $400, and you have to rent skis for each day, which costs an extra $20 per day. Hence, the total cost per day with the season ski pass is $400/number of days skiing + $20.
To find the number of days skiing needed to make the season pass cheaper, we need to set up an equation:
$400/number of days skiing + $20 = $87
To solve this equation, we can subtract $20 from both sides:
$400/number of days skiing = $87 - $20
$400/number of days skiing = $67
Now, we can isolate the number of days skiing by multiplying both sides of the equation by the reciprocal of $67, which is 1/67:
(number of days skiing) = $400 / $67
(number of days skiing) = 5.97 (approximately)
Since you cannot have a fractional number of days skiing, you need to round up to the nearest whole number. Therefore, the skier would need to go skiing for at least 6 days to make the season ski pass less expensive than the daily passes.