A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $78. A season ski pass costs $450. The skier would have to rent skis with either pass for $25 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?
Let x be the number of days the skier would have to go skiing in order to make the season pass less expensive than the daily passes.
The cost of renting skis for x days would be 25x.
For the daily pass, the cost for x days of skiing would be 78x.
For the season pass, the total cost for x days of skiing would be 450 + 25x.
Setting up an inequality, we get 450 + 25x < 78x.
Combining like terms, we get 450 < 53x.
Dividing both sides by 53, we get 8.49 < x.
Rounded up, x is at least 9 days.
Thus, the skier would have to go skiing for at least 9 days in order to make the season pass less expensive than the daily passes. Answer: \boxed{9}.
To determine the number of days the skier would have to go skiing in order to make the season pass less expensive than the daily passes, we can set up an equation.
Let's assume that the number of days the skier would go skiing is represented by 'd'.
The cost of using daily passes for 'd' days would be: 78d.
The cost of a season ski pass would be: 450.
The cost of renting skis for 'd' days would be: 25d.
Setting up the equation:
78d + 25d = 450
Combining like terms:
103d = 450
Now, divide both sides of the equation by 103:
d = 4.37
Since we can't have a fraction of a day, we can round the answer up to the nearest whole number. Therefore, the skier would have to go skiing for at least 5 days in order to make the season pass less expensive than the daily passes.