skier problem for math

Question

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs

​$72.

A season ski pass costs

​$350.

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

350 = 72D

D = 350/72 = 175/36 = 4.86 days to have cost the same for either pass

5 days or more makes the season pass less expensive than pay for 5 or more daily passes

for 5 days, it costs 72x5 =$360 for daily passes> $350 for the season pass

for 4 days, it cost 72x4 = $288 < $350

Unless, the $30 ski rental rate is per day for the daily pass and one flat $30 ski fee per season for the season pass.

then

350 +30 = 72D + 30D

102D = 380

D= 380/102 = about 3.7 days as the break even point

then 4 or more days makes the season pass cheaper