Question

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$78. A season ski pass costs ​$300. 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?

Answer 1

`4` days.

`$432 ("daily + ski rental") > $420 ("seasonal + ski rental")`

Explanation:

If a daily pass costs `$78` and he also has to pay `$30` a day for ski rental, it is `$78 + $30` for one day with the daily pass, or `$108`.

In 3 days `(3xx$108)`, he will have spent `$324`.

However, if the skier were to buy the season pass, he would also have to pay for ski rental per day, adding `3` days `xx $30` to the original `$300` season pass, finally totaling `$390`.

This means the skier must go skiing for at least `4` days to surpass the cost of the season pass.

`4` days of one-day passes plus daily rental ski costs total `4` days `xx $(78 +30) = $432`.

Season pass plus `4` days of ski rental costs `$300 + 3 xx $40`, which equals `$420`.