please help me 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.

Answer 1

Part A)

Let:
x = number of hours bowled
y = total cost

For Fun Time Bowling:
Fun Time's total cost (y) can be represented by the equation:
y = 3 + 9x

For Strike Zone Bowling:
Strike Zone's total cost (y) can be represented by the equation:
y = 5 + 8x

Part B)

To determine when both Bowling Alleys will cost the same amount, we can equate the two equations:

3 + 9x = 5 + 8x

Next, we can solve for x:

9x - 8x = 5 - 3
x = 2

Now we can substitute x back into one of the original equations to find the corresponding total cost, y:

y = 3 + 9(2)
y = 3 + 18
y = 21

Therefore, both Bowling Alleys will cost the same amount after 2 hours of bowling, with a total cost of $21.