A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $80. A season ski pass costs $350. The skier would have to rent skis with either pass for $30 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?
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 each option.
For the daily pass:
Cost per day = $80 (daily pass) + $30 (ski rental) = $110
For the season pass:
Cost per day = $350 (season pass) / number of days
To find the number of days needed to make the season pass less expensive, we can set up the following equation:
$110 * number of days = $350
Divide both sides by $110:
number of days = $350 / $110 ≈ 3.18
Since the number of days must be a whole number, the skier would need to go skiing for at least 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 can set up an equation.
Let N be the number of days the skier would have to go skiing.
For daily passes:
Cost of daily pass = $80 + $30 (for ski rental) = $110
For season pass:
Cost of season pass = $350 + ($30 × N) (for ski rentals on each day)
We need to find the value of N that makes the season pass less expensive than the daily pass. So we set up the inequality:
$110 × N > $350 + ($30 × N)
Now we can solve for N:
110N > 350 + 30N
80N > 350
N > 350/80
N > 4.375
Since N represents the number of days the skier would have to go skiing, it must be a whole number. Therefore, 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.