A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $73. 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' days.
With a daily pass, the total cost for skiing for 'x' days would be 73x + 20x.
With a season pass, the total cost for skiing for 'x' days would be 400 + 20x.
We need to find when the season pass becomes less expensive than the daily passes, so we need to solve the following equation:
400 + 20x < 73x + 20x
400 < 93x
400/93 < x
x > 4.3
Since 'x' represents the number of days the skier goes skiing, it cannot be a fraction or a decimal. Therefore, the skier would have to go skiing for 5 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 can set up an equation.
Let's assume the skier goes skiing for "x" number of days.
The cost of using a daily pass for "x" number of days would be 73x dollars.
The cost of renting skis for "x" number of days would be 20x dollars.
Therefore, the total cost of using a daily pass for "x" number of days would be 73x + 20x = 93x dollars.
The cost of a season pass is 400 dollars.
To make the season pass less expensive, we need to find the value of "x" when 93x is less than 400.
So, we can set up the inequality:
93x < 400
Now, we can solve the inequality:
x < 400/93
x < 4.30 (rounded to two decimal places)
Since the number of days must be a whole number, the skier would have to go skiing for 4 days to make the season pass less expensive than the daily passes.