Question

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $65. A season pass costs $400. 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 pass?

Answer 1

Let x be the number of days.

Daily pass:
65x + 30x
95x

Season pass:
400 + 30x

95x > 400 + 30x
65x > 400
x > 6.15

The number of days can't be 6.15, so you must round. You can't go down because then the price will be more expensive, so you have to round up.

It would take 7 days until the season pass is less expensive than the daily pass.
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You can check this by plugging in the x.

95x > 400 + 30x
95(7) > 400 + 30(7)
665 > 400 + 210
665 > 600
The daily pass is more expensive than the season pass.