Pls help.

Question

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.

2) 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.
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? (select one)

A) 1 hour

B) 3 hours

C) 2 hours

D) Never

Answer 1

Part A:
Let's define the variables:
Let "x" represent the number of hours bowled.
Let "y1" represent the cost of bowling at Fun Time Bowling.
Let "y2" represent the cost of bowling at Strike Zone Bowling.

Using the given information, we can write the system of equations as follows:
For Fun Time Bowling:
y1 = 9x + 3

For Strike Zone Bowling:
y2 = 8x + 5

Part B:
To determine when both Bowling Alleys will cost the same amount, we can set y1 equal to y2 and solve for x:

9x + 3 = 8x + 5

Subtract 8x from both sides:

x + 3 = 5

Subtract 3 from both sides:

x = 2

So, when x = 2 (or after 2 hours of bowling), both Bowling Alleys will cost the same amount.

2) The correct statements are:

A) The rate of change for each Bowling Alley represents the cost of bowling per hour.
D) The rate of change for Fun Time bowling is $8.

The rate of change represents how the cost changes with each additional hour of bowling. In this case, the rate of change for Fun Time Bowling is $8 per hour, and the rate of change for Strike Zone Bowling is $9 per hour.

3) When bowling at Strike Zone Bowling would be a better deal than Fun Time Bowling:

B) 3 hours

After 3 hours of bowling, the cost at Strike Zone Bowling would be lower than the cost at Fun Time Bowling.