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.

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.

Answer 1

Part A:

Let x be the number of hours bowled.
Let F(x) be the cost in dollars for Fun Time Bowling.
Let S(x) be the cost in dollars for Strike Zone Bowling.

For Fun Time Bowling:
F(x) = 3 + 9x

For Strike Zone Bowling:
S(x) = 5 + 8x

Part B:
To determine when both bowling alleys will cost the same amount, we need to set F(x) equal to S(x) and solve for x:
3 + 9x = 5 + 8x

Subtracting 8x from both sides:
9x - 8x = 5 - 3
x = 2

Therefore, Fun Time Bowling and Strike Zone Bowling will cost the same amount after 2 hours of bowling.