Question

a skier is trying to decide whether or not to buy a season ski pass. a daily pass costs $80. a season ski pass costs $450. 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? the skier would have to go skiing \\(\square\\) days. (type a whole number.)

Explanation:

Step1: Define variables and cost equations

Let $x$ = number of skiing days.
Daily pass total cost: $C_d = (80 + 20)x = 100x$
Season pass total cost: $C_s = 450 + 20x$

Step2: Set up inequality for cost savings

We need $C_s < C_d$:
$$450 + 20x < 100x$$

Step3: Solve the inequality

Subtract $20x$ from both sides:
$$450 < 80x$$
Divide both sides by 80:
$$x > \frac{450}{80} = 5.625$$

Step4: Round up to whole number

Since days are whole numbers, $x=6$.

Answer:

6