SOLUTION: A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $67. A season ski pass costs $350. The skier would have to rent skis with either pass for $2

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $67. A season ski pass costs $350. The skier would have to rent skis with either pass for $2      Log On


   

Question 1191959: A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $67. A season ski pass costs $350. 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?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


Cost equation for daily pass:  



    C_daily = 67x + 25x = 92x,  where x = # days skied





Cost equation for season pass:

    C_season = 350 + 25x



We wish to find x such that C_season < C_daily



   350 + 25x < 92x

       350   < 67x



       350/67 < x    

        5.224 < x     



    x = 6 ski days





Sanity check...





#days skied     Daily pass cost     Season pass cost

    4             368                   450

    5             460                   475

    6             552                   500    <----  Season pass becomes cheaper





If you plot the two cost equations, the point where they cross is the point where the season pass becomes more cost effective (well, the nearest integer above where they cross).   



The green line represents the season pass cost equation: