A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $64. A season ski pass costs $300. 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?
The skier would have to go skiing enter your _____ days.
Let's assume the skier would go skiing for x number of days.
With the daily pass, the skier would spend:
64(x) on daily passes and
25(x) on ski rentals
So the total cost with the daily pass would be:
64x + 25x = 89x
With the season pass, the skier would spend:
300 on the season pass and
25(x) on ski rentals
So the total cost with the season pass would be:
300 + 25x
To make the season pass less expensive than the daily passes, we can set up the following equation:
300 + 25x < 89x
Now, let's solve for x:
Subtract 25x from both sides:
300 < 89x - 25x
300 < 64x
Divide both sides by 64:
300/64 < x
4.6875 < x
Since the skier cannot go skiing for a fraction of a day, 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 find the number of days the skier would have to go skiing in order to make the season pass less expensive than the daily passes, let's set up an equation.
Let's assume the skier goes skiing for "x" number of days.
With a daily pass, the skier has to pay $64 per day for skiing and an additional $25 per day for renting skis. So, the cost of skiing for "x" days with daily passes would be 64x + 25x.
With a season pass, the skier pays a one-time cost of $300 for the pass and an additional $25 per day for renting skis. So, the cost of skiing for "x" days with a season pass would be 300 + 25x.
We now need to find the value of "x" where the cost of skiing with daily passes is equal to or exceeds the cost of skiing with a season pass.
64x + 25x = 300 + 25x
Simplifying the equation:
89x = 300
Dividing both sides by 89:
x = 300/89
Using a calculator, we find that x is approximately 3.37 (rounded to two decimal places).
Therefore, the skier would have to go skiing for 3.37 (or around 3 to 4) 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 daily passes for those days versus the cost of purchasing a season pass.
Let's calculate the total cost of using daily passes first:
Total cost of using daily passes = (cost of daily pass + cost of ski rentals) * number of days
According to the information given, the cost of a daily pass is $64, and the cost of ski rentals is $25 per day. Therefore, the equation to calculate the total cost of using daily passes would be:
Total cost of using daily passes = (64 + 25) * number of days
Now let's calculate the cost of purchasing a season pass:
Cost of purchasing a season pass = cost of season pass + (cost of ski rentals * number of days)
According to the information given, the cost of a season pass is $300, and the cost of ski rentals is $25 per day. Therefore, the equation to calculate the cost of purchasing a season pass would be:
Cost of purchasing a season pass = 300 + (25 * number of days)
To find out when the season pass becomes less expensive than the daily passes, we need to set the two equations equal to each other and solve for the number of days:
(64 + 25) * number of days = 300 + (25 * number of days)
Now we can solve for the number of days by isolating the variable:
64 * number of days + 25 * number of days = 300 + 25 * number of days
(64 + 25) * number of days = 300 + 25 * number of days
89 * number of days = 300 + 25 * number of days
64 * number of days = 300
number of days = 300 / 64
Using this formula, the skier would have to go skiing for approximately 4.69 days (approximately 5 days) to make the season pass less expensive than the daily passes.
So, the skier would have to go skiing for 5 days in order to make the season pass less expensive than the daily passes.