skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $65. A season ski pass costs 5450. The skier would lave 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.
With the daily pass, the skier would have to spend $65 * x for daily passes.
However, the skier would also have to spend $20 * x for renting skis.
So, the total cost with the daily passes is $65x + $20x = $85x.
On the other hand, the cost of the season ski pass is $5450.
If the skier purchases the season ski pass, they won't have to pay the daily pass fee ($65x) or the ski rental fee ($20x).
Therefore, we need to find the value of "x" when $5450 < $85x.
Dividing both sides of the inequality by $85, we get:
$5450 / $85 < x
64.12 < x
So, the skier would have to go skiing for at least 65 days 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 calculate the break-even point.
Let's assume the skier goes skiing for 'x' days.
The cost of daily passes for 'x' days would be: $65 * x
The cost of renting skis for 'x' days would be: $20 * x
Therefore, the total cost of using daily passes would be: ($65 * x) + ($20 * x) = $85 * x
The cost of the season ski pass is $5450.
Now, we need to find the value of 'x' that makes the season pass less expensive than daily passes:
$5450 < $85 * x
Dividing both sides of the inequality by $85:
x > $5450 / $85
x > 64.12
Since the skier cannot go skiing for a fraction of a day, the skier would have to go skiing for at least 65 days to make the season pass less expensive than the daily passes.
To determine the number of 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 purchasing daily passes for those days with the cost of the season pass.
Let's calculate the total cost of purchasing daily passes:
Total cost of daily passes = Number of days * Cost of daily pass
Now, let's consider the additional cost of renting skis for each pass:
Total cost of renting skis = Number of days * Cost of ski rental
Finally, we can calculate the total cost of purchasing daily passes and renting skis:
Total cost of purchasing daily passes and renting skis = Total cost of daily passes + Total cost of renting skis
To find the number of days required to make the season pass less expensive, we need to solve the following equation:
Total cost of purchasing daily passes and renting skis = Cost of season pass
Let's plug in the given values:
Daily pass cost = $65
Season pass cost = $5450
Ski rental cost = $20
Now, we solve the equation:
Number of days * $65 + Number of days * $20 = $5450
Simplifying the equation:
$65d + $20d = $5450
where 'd' represents the number of days the skier needs to go skiing.
Combining like terms:
$85d = $5450
To isolate 'd', divide both sides by $85:
d = $5450 / $85
d ≈ 64.12
Therefore, the skier would need to go skiing for approximately 64 days in order for the season pass to be less expensive than purchasing daily passes. However, since a fractional number of days is not practical, the skier would likely need to go skiing for at least 65 days to make the season pass more cost-effective.