Fun time bowling has a shoe rental fee of three dollars and nine dollars per hour strike zone bowling has a shoe rental fee of five dollars and eight dollars per hour
Part A) defined 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.
Part A)
Let x represent the number of hours spent bowling at Fun Time Bowling.
Let y represent the number of hours spent bowling at Strike Zone Bowling.
At Fun Time Bowling:
The cost for shoe rental is $3.
The cost for bowling per hour is $9.
So, the total cost at Fun Time Bowling is 3 + 9x.
At Strike Zone Bowling:
The cost for shoe rental is $5.
The cost for bowling per hour is $8.
So, the total cost at Strike Zone Bowling is 5 + 8y.
Therefore, the system of equations representing each bowling alley is:
For Fun Time Bowling: 3 + 9x
For Strike Zone Bowling: 5 + 8y
Part B)
To determine when both bowling alleys will cost the same amount, we can set the total costs at each bowling alley equal to each other and solve for the hours.
3 + 9x = 5 + 8y
To solve this equation using the substitution method, we can solve one of the equations for x or y and substitute it into the other equation. Let's solve the equation 3 + 9x = 5 + 8y for x:
9x - 8y = 5 - 3
9x - 8y = 2
9x = 2 + 8y
9x = 8y + 2
x = (8y + 2)/9
Now, substitute this value of x into the other equation:
3 + 9((8y + 2)/9) = 5 + 8y
3 + 8y + 2 = 5 + 8y
8y + 5 = 5 + 8y
In this case, we can see that the variable "y" cancels out. This means that the equation is dependent and that there are infinitely many solutions. In other words, both bowling alleys will cost the same amount for any value of y.
Therefore, the solution in terms of y is that both bowling alleys will cost the same amount regardless of how many hours are spent bowling at each alley. The cost will be equal if the shoe rental fee is $5 and the cost per hour of bowling is $8.