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.
show your work
Part A:
Let x be the number of hours of bowling.
For Fun Time Bowling, the total cost (C) can be represented by the equation C = 3 + 9x.
For Strike Zone Bowling, the total cost (C) can be represented by the equation C = 5 + 8x.
Part B:
To find when both Bowling Alleys will cost the same amount, we set the two cost equations equal to each other:
3 + 9x = 5 + 8x
Subtract 8x from both sides:
3 + x = 5
Subtract 3 from both sides:
x = 2
Therefore, both Bowling Alleys will cost the same amount after 2 hours of bowling.
Which of the following are true statements? Select all the apply.(2 points)
Responses
The rate of change for each Bowling Alley represents the cost of bowling per hour
The y-intercepts of the graphs represents the total cost
The rate of change for FunTime bowling is $8
The y-intercept for Strike Zone Bowling is (0,5)
Question 3
When would Bowling at Strike Zone be a better deal then Fun Time?(1 point)
Responses
1 hour
3 hours
Never
2 hours
The correct answers are:
- The rate of change for each Bowling Alley represents the cost of bowling per hour
- The y-intercepts of the graphs represents the total cost
As for the second part of the question:
- When would Bowling at Strike Zone be a better deal than Fun Time?
Bowling at Strike Zone would be a better deal than Fun Time when the cost at Strike Zone is lower than the cost at Fun Time. To determine this, we need to compare the total cost equations for each bowling alley:
For Fun Time Bowling: C = 3 + 9x
For Strike Zone Bowling: C = 5 + 8x
We can solve for x to find the number of hours at which Strike Zone is a better deal than Fun Time:
3 + 9x > 5 + 8x
Subtract 8x from both sides:
3 + x > 5
Subtract 3 from both sides:
x > 2
Therefore, Strike Zone would be a better deal than Fun Time after 2 hours of bowling.