a skier is trying to decide whether or not to buy a season ski pass. a daily pass costs $68. a season ski…

a skier is trying to decide whether or not to buy a season ski pass. a daily pass costs $68. a season ski pass costs $400. 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 days. (type a whole number.)

a skier is trying to decide whether or not to buy a season ski pass. a daily pass costs $68. a season ski pass costs $400. 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 days. (type a whole number.)

Answer

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of days of skiing. The cost of daily passes including ski - rental is $C_d=(68 + 20)x=88x$. The cost of the season pass including ski - rental is $C_s=400+20x$.

Step2: Set up the inequality

We want to find when the season pass is less expensive than the daily passes, so we set up the inequality $400 + 20x<88x$.

Step3: Solve the inequality

Subtract $20x$ from both sides: $400<88x - 20x$, which simplifies to $400<68x$. Then divide both sides by 68: $x>\frac{400}{68}=\frac{100}{17}\approx5.88$.

Step4: Find the whole - number value

Since $x$ represents the number of days and it must be a whole number, and $x>5.88$, the smallest whole number for $x$ is 6.

Answer:

6