Question

1) 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.
please summarize at the end.

2) Which of the following are true statements? Select all the apply.(2 points) a) The rate of change for each Bowling Alley represents the cost of bowling per hour. b) The y-intercepts of the graphs represents the total cost. c) The y-intercept for Strike Zone Bowling is (0,5). d) The rate of change for FunTime bowling is $8.

3) When would Bowling at Strike Zone be a better deal then Fun Time?(1 point)

A) 1 hour

B) Never

C) 2 hours

D) 3 hours

Answer 1

Part A)
Let x represent the number of hours bowled.
Let F(x) represent the cost at Fun Time Bowling.
Let S(x) represent the cost at Strike Zone Bowling.

The system of equations is:
F(x) = 3 + 9x
S(x) = 5 + 8x

Part B)
To find 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

Subtracting 8x from both sides:
3 + x = 5

Subtracting 3 from both sides:
x = 2

Therefore, both Bowling Alleys will cost the same amount after 2 hours.

Summary:
1) The variables are x (number of hours bowled), F(x) (cost at Fun Time Bowling), and S(x) (cost at Strike Zone Bowling).
The system of equations is F(x) = 3 + 9x and S(x) = 5 + 8x.

2) The true statements are:
a) The rate of change for each Bowling Alley represents the cost of bowling per hour.
b) The y-intercepts of the graphs represent the total cost.
c) The y-intercept for Strike Zone Bowling is (0,5).

3) Bowling at Strike Zone is a better deal than Fun Time after 2 hours (option C).