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

Answer 1

Part A)
Let's define the variables:
Let x be the number of hours.
Let F(x) be the total cost at Fun Time Bowling.
Let S(x) be the total cost at Strike Zone Bowling.

For Fun Time Bowling:
The shoe rental fee is $3, and there is an additional $9 charge per hour, so the cost function is:
F(x) = 3 + 9x

For Strike Zone Bowling:
The shoe rental fee is $5, and there is an additional $8 charge per hour, so the cost function is:
S(x) = 5 + 8x

Part B)
To find when both bowling alleys will cost the same amount, we can set the cost functions equal to each other and solve for x:
F(x) = S(x)
3 + 9x = 5 + 8x
Subtract 8x from both sides of the equation:
3 + x = 5
Subtract 3 from both sides of the equation:
x = 2

So, both bowling alleys will cost the same amount when x = 2, which means after 2 hours of bowling.