A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$64. A season ski pass costs ​$300. 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?

Question

The skier would have to go skiing enter your _____ days.

Answer 1

Let's assume the skier would go skiing for x number of days.

With the daily pass, the skier would spend:
64(x) on daily passes and
25(x) on ski rentals

So the total cost with the daily pass would be:
64x + 25x = 89x

With the season pass, the skier would spend:
300 on the season pass and
25(x) on ski rentals

So the total cost with the season pass would be:
300 + 25x

To make the season pass less expensive than the daily passes, we can set up the following equation:

300 + 25x < 89x

Now, let's solve for x:

Subtract 25x from both sides:
300 < 89x - 25x
300 < 64x

Divide both sides by 64:
300/64 < x
4.6875 < x

Since the skier cannot go skiing for a fraction of a day, 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.