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
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.