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?

1 Answer
Feb 24, 2018

Answer:

#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#.