Alpine Valley charges $10/hr for lessons and $40 for the lift ticket and snowboard rental.
Chicopee Hills charges $20/hr which includes lessons, lift ticket and rentals. Which resort would you choose?
Equation A: y=. X+
Equation B: y=. X+
Decide on a reasonable starting point and ending point for the x value (quantity or time)
A: y=10x+40
B: y=20x
To determine which resort would be a better choice, we need to compare the total cost of a visit to each resort.
Let's assume that "X" represents the quantity of hours spent at the resort.
For Alpine Valley, the cost includes $10 per hour for lessons plus $40 for the lift ticket and snowboard rental. So, the equation for Alpine Valley would be:
Cost_A = 10X + 40
For Chicopee Hills, the cost is a flat rate of $20 per hour, which includes lessons, lift ticket, and rentals. Therefore, the equation for Chicopee Hills would be:
Cost_B = 20X
To compare the two options, we can evaluate the total cost for different values of X within a reasonable range.
Let's choose a starting point of X = 1 hour and an ending point of X = 5 hours.
For Alpine Valley:
Cost_A(1) = 10(1) + 40 = $50
Cost_A(2) = 10(2) + 40 = $60
Cost_A(3) = 10(3) + 40 = $70
Cost_A(4) = 10(4) + 40 = $80
Cost_A(5) = 10(5) + 40 = $90
For Chicopee Hills:
Cost_B(1) = 20(1) = $20
Cost_B(2) = 20(2) = $40
Cost_B(3) = 20(3) = $60
Cost_B(4) = 20(4) = $80
Cost_B(5) = 20(5) = $100
Now that we have the costs for different values of X, we can compare them.
If you plan on spending only 1 hour, Chicopee Hills is the better choice as it costs $20 there compared to $50 at Alpine Valley.
For 2 hours, Chicopee Hills still costs less at $40 compared to $60 at Alpine Valley.
However, when you spend 3 hours, Chicopee Hills and Alpine Valley both cost $60. At this point, either resort would be equally affordable.
If you plan on spending 4 hours, Chicopee Hills becomes more expensive at $80 compared to $80 at Alpine Valley. Here, Alpine Valley is the better choice.
Finally, if you plan on spending 5 hours, Chicopee Hills costs $100 whereas Alpine Valley costs $90. In this case, Alpine Valley would be the more economical choice.
Therefore, based on the comparison of costs for different time durations, it is more cost-effective to choose between the two resorts based on how many hours you plan to spend.