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

Question

need homework help ASAP!

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $70. A season ski pass costs $300. The skier would have to rent skis with either pass for $20 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

To solve this problem you must set up an inequality where each side of the equation represents the cost associated with each pass.

COST WITH DAILY PASS = 90d, where 90 represents the cost of renting skis and paying for the pass and d represents the number of days the skier goes skiing.

COST WITH SEASON PASS = 300 + 20d, where 300 represents the cost of the pass, 20 is the cost of the ski rental, multiplied by the number of days the skis are rented.

SET UP THE INEQUALITY, we want to determine at which value of d the season pass is less expensive than paying for a daily pass. Therefore we set up the inequality this way:

90d > 300+20d

TO SOLVE FOR d

90d > 300+20d

70d > 300

d > 4.28

This means that it is less expensive to buy a season pass as long as the skier goes 4.28 times, but since he can't go 4.28 days, we must round up to the next whole number, which is 5.

As long as the skier goes 5 days, it is less expensive to have a season pass.