For what number of days is the cost for a season pass equal to the cost for daily passes?
6 days
Practice makes perfect
We have been asked to calculate the number of days it would take for the season pass to be less expensive than the daily pass. To do this, we need to write and solve an equation where both sides are expressions representing the total costs. Let d represent the number of days the skier goes skiing.
Phrase
Expression
Cost for d daily passes
$67d
Cost for a season pass
$350
To figure out when one cost is higher, we can first find out when they are equal. If the two costs are equal on d days, then the two expressions can be set equal to form an equation.
67d= 350
Now we can solve for d. Please note that the daily cost of ski rental is not important. It will cost the same each day, no matter which kind of pass is bought.
Now that d is isolated, we can see that the costs of the passes are equal when d is approximately 5.22. Because the skier cannot purchase a partial day of skiing, let's determine the cost of the day pass for 5 days and 6 days.
d
67d
Cost
5
67 ( 5)
$335
6
67( 6)
$402
From the work above, we can see that the cost of the day pass is less than the cost of the season pass for 5 days or fewer, and more than the cost of the season pass for 6 days or more. Thus, the skier must ski for at least 6 days to make the season pass less expensive.
