Algebra Question

Question

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?

Answer 1

d = days skiing

cost of skiing daily pass = 68d + 20d

cost of skiing season pass = 400 + 20d

when is season pass less expensive?

68d + 20d > 400 + 20d, subtract three 20d

68d > 400, divide by 68 result

d > 5.882352941

Therefore at least 6 days

Answer 2

Question: 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?

Answer: Let's compare entry and rental fees for both passes, starting from the fourth day.

68 x 4 = 272 for entry, plus 20(4) to rent skis for four days = 352 with daily pass

versus

20 x 4 = 80 for skis, plus 400 flat for the season pass = 480 with a season pass. Daily pass cheaper after four days.

68 x 5 = 340 for entry, plus 20(5) to rent skis for five days = 440 with daily pass

versus

20 x 5 = 100 for skis, plus 400 flat for the season pass = 500 with a season pass. Daily pass cheaper after five days.

68 x 6 = 408 for entry, plus 20(6) to rent skis for six days = 528 with daily pass

versus

20 x 6 = 120 for skis, plus 400 flat for the season pass = 520 with a season pass. Season pass cheaper after six days.

Here's another way to think of it. Let x represent the number of days, and y represent total cost:

SEASON PASS: y = $20x + $400 <--- $400 is flat, one-time, and so not multiplied by # of days

DAILY PASS: y = $20x + $68x ---> y = $88x

88x = 20x + 400

68x = 400

x = 5.88

This will be rounded up since the ski resort counts whole-number days, and not partial days; don't round down, since this 5.88 is a meeting point of the two equations, when the two passes cost exactly the same. Rounding down to five days keeps the season pass more expensive.



Go ski for at least six days to make the season pass less expensive than the daily passes. Make a week-long vacation of it!

Answer 3

Let x = number of days of skiing

Cost with season pass = 20x + 400

Cost with daily pass = 20x + 68x = 88x

Costs are the same when 88x = 20x + 400

68x = 400

x = 5.88

If the skier plans to ski 6 days or more, then buy the season pass. Otherwise, do the day by day option

.