A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $70. 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?
$400 / $70 = ?
round up for the number of days
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 skiing with the season pass to the total cost of skiing with daily passes.
Let's break down the costs involved:
- Cost of a daily pass: $70
- Cost to rent skis with a daily pass: $20
Therefore, the total cost of skiing for one day with a daily pass is $70 + $20 = $90.
Now, let's consider the cost of the season pass:
- Cost of a season pass: $400
- Cost to rent skis with the season pass: $20
With the season pass, the skier can ski for the entire season without any additional cost, so the total cost of skiing remains constant at $20 per day.
To find out how many days the skier would have to go skiing to make the season pass less expensive than the daily passes, we need to compare the costs. We can set up an equation:
Number of days skiing x Cost per day with daily pass = Cost of season pass
Let's represent the number of days skiing as "d":
d x $90 = $400 + $20d
Simplifying the equation:
90d = 400 + 20d
90d - 20d = 400
70d = 400
Now, we can solve for "d" by dividing both sides of the equation by 70:
d = 400 / 70
d = 5.71...
Since skiing on a fraction of a day doesn't make sense, we can round up to the nearest whole number. Therefore, the skier would have to go skiing for at least 6 days in order to make the season pass less expensive than the daily passes.