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)

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. Upload a picture of your handwritten work. (6 points)

Answer 1

Let's define the variables:

- Let's use F for Fun Time Bowling.
- Let's use S for Strike Zone Bowling.
- Let's use x for the number of hours.
- Let's use C for the cost.

Part A:
1. For Fun Time Bowling:
- Shoe rental fee: $3
- Cost per hour: $9
The equation that represents the cost at Fun Time Bowling is:
C(F) = 3 + 9x

2. For Strike Zone Bowling:
- Shoe rental fee: $5
- Cost per hour: $8
The equation that represents the cost at Strike Zone Bowling is:
C(S) = 5 + 8x

Part B:
To find when both Bowling Alleys will cost the same amount, we can set the two equations equal to each other:
C(F) = C(S)
3 + 9x = 5 + 8x

Now we can solve for x:
9x - 8x = 5 - 3
x = 2

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

(Note: I apologize for not being able to upload a picture of the handwritten work as an AI text-based model. However, I hope the provided solution is clear and helpful.)