Fun Time Bowling has a shoe rental fee of $3 and $9 per hour. Strike Zone Bowling has a shoe rental fee of $5 and $8 per hour.
Part A) Define the variables and write a system of equations to represent each Bowling Alley.
Part B) Use the substitution method to determine when both Bowling Alleys will cost the same amount. Make sure to show work to receive credit. Upload a picture of your handwritten work.
(6 points)
Which of the following are true statements? Select all the apply. (2 points)
The rate of change for each Bowling Alley represents the cost of bowling per hour
The y-intercepts of the graphs represents the total cost
The y-intercept for Strike Zone Bowling is (0,5)
The rate of change for FunTime bowling is $8
Part A:
Let's define the variables:
F = Fun Time Bowling total cost (in dollars)
S = Strike Zone Bowling total cost (in dollars)
h = hours of bowling
With this, we can write the system of equations:
For Fun Time Bowling:
F = 3 (shoe rental fee) + 9h (cost per hour)
For Strike Zone Bowling:
S = 5 (shoe rental fee) + 8h (cost per hour)
Part B:
To determine when both Bowling Alleys will cost the same amount, we can set F equal to S and solve for h:
3 + 9h = 5 + 8h
Subtract 8h from both sides:
3 + h = 5
Subtract 3 from both sides:
h = 2
So, both Bowling Alleys will cost the same amount when bowling for 2 hours.
Now, let's check some statements:
The rate of change for each Bowling Alley represents the cost of bowling per hour: True. The coefficient of h in each equation represents the cost per hour.
The y-intercepts of the graphs represents the total cost: False. The y-intercepts represent the total cost when bowling for 0 hours, which is just the shoe rental fee.
The y-intercept for Strike Zone Bowling is (0,5): True. The y-intercept of the equation for Strike Zone Bowling is 5, which represents the shoe rental fee.
The rate of change for FunTime bowling is $8: True. The coefficient of h in the equation for FunTime Bowling is 9, which represents the cost per hour.