A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $77. A season ski pass costs $400. 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?
Let's denote the number of days the skier would go skiing as X.
The cost of renting skis for each day would be $25*X.
The total cost of using daily passes would be 77*X + 25*X.
The cost of the season pass would be $400 + 25*X.
We want to find the number of days, X, such that 400 + 25*X < 77*X + 25*X.
Simplifying the equation, we get: 400 + 25*X < 102*X.
Subtracting 25*X from both sides, we get: 400 < 77*X.
Dividing both sides by 77, we get: 400/77 < X.
Calculating the result, we get: X > 5.195.
Since we can't go skiing for a fraction of a day, the skier would have to go skiing for at least 6 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 cost of purchasing daily passes for each day versus the cost of purchasing a season pass.
Let's calculate the cost of purchasing daily passes for the required number of days:
Cost of daily pass per day = $77
Rental skis per day = $25
Total cost of one day of skiing with daily pass = $77 + $25 = $102
Now, let's calculate how many days the skier needs to go skiing for the daily passes to be less expensive than the season pass:
Total cost of season pass = $400
Total cost of renting skis with season pass = $25 x number of days
To make the season pass less expensive than the daily passes, the inequality would be:
$102 x number of days > $400 + $25 x number of days
Simplifying the inequality:
$102 x number of days > $400
Divide both sides by $102:
number of days > $400 / $102
Using long division:
$400 divided by $102 = 3 with a remainder of 94
Therefore, the skier would have to go skiing for at least 4 days in order to make the season pass less expensive than purchasing daily passes.