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) Responses The rate of change for FunTime bowling is $8 The rate of change for FunTime bowling is $8 The y-intercept for Strike Zone Bowling is (0,5) The y-intercept for Strike Zone Bowling is open paren 0 comma 5 close paren The y-intercepts of the graphs represents the total cost The y-intercepts of the graphs represents the total cost The rate of change for each Bowling Alley represents the cost of bowling per hour The rate of change for each Bowling Alley represents the cost of bowling per hour Question 3 When would Bowling at Strike Zone be a better deal then Fun Time?(1 point) Responses 2 hours 2 hours Never Never 1 hour 1 hour 3 hours
Part A:
Let x represent the number of hours bowled.
Let F(x) represent the total cost of bowling at Fun Time Bowling.
Let S(x) represent the total cost of bowling at Strike Zone Bowling.
The system of equations is as follows:
F(x) = 3 + 9x
S(x) = 5 + 8x
Part B:
To determine when both Bowling Alleys will cost the same amount, we set F(x) equal to S(x) and solve for x:
3 + 9x = 5 + 8x
9x - 8x = 5 - 3
x = 2
Therefore, both Bowling Alleys will cost the same amount when 2 hours of bowling.
True statements:
- The rate of change for FunTime bowling is $8
- The y-intercept for Strike Zone Bowling is (0,5)
- The y-intercepts of the graphs represents the total cost
- The rate of change for each Bowling Alley represents the cost of bowling per hour
When bowling at Strike Zone would be a better deal than Fun Time:
- 2 hours