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 represent the number of hours spent bowling.
Let F(x) represent the cost of bowling at Fun Time Bowling.
Let S(x) represent the cost of bowling at Strike Zone Bowling.
Based on the given information, we can write the following equations:
For Fun Time Bowling:
F(x) = 3 (shoe rental fee) + 9x (cost per hour)
For Strike Zone Bowling:
S(x) = 5 (shoe rental fee) + 8x (cost per hour)
Part B)
To determine when both bowling alleys will cost the same amount, we need to find the values of x for which F(x) = S(x).
Setting the two equations equal to each other:
3 + 9x = 5 + 8x
Simplifying the equation:
9x - 8x = 5 - 3
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 rate of change for each Bowling Alley represents the cost of bowling per hour
The rate of change for FunTime bowling is $8
The rate of change for FunTime bowling is $8
The y-intercepts of the graphs represents the total cost
The y-intercepts of the graphs represents the total cost
The y-intercept for Strike Zone Bowling is (0,5)
The rate of change for each Bowling Alley represents the cost of bowling per hour. (Correct)
The rate of change for FunTime bowling is $8. (Incorrect, the rate of change for FunTime bowling is $9 per hour)
The y-intercepts of the graphs represent the total cost. (Correct)
The y-intercept for Strike Zone Bowling is (0,5). (Incorrect, the y-intercept for Strike Zone Bowling is (0,5) only represents the shoe rental fee and does not include the cost per hour)
When would Bowling at Strike Zone be a better deal then Fun Time?(1 point)
Responses
1 hour
1 hour
3 hours
3 hours
Never
Never
2 hours
To determine when bowling at Strike Zone would be a better deal than Fun Time, we can compare the costs for a given number of hours of bowling.
Let's compare the costs for 1 hour of bowling at each alley:
- Fun Time Bowling: $3 (shoe rental fee) + $9 (cost per hour) = $12
- Strike Zone Bowling: $5 (shoe rental fee) + $8 (cost per hour) = $13
In this case, Fun Time Bowling is the better deal.
Now let's compare the costs for 3 hours of bowling at each alley:
- Fun Time Bowling: $3 (shoe rental fee) + $9 * 3 (cost per hour) = $30
- Strike Zone Bowling: $5 (shoe rental fee) + $8 * 3 (cost per hour) = $29
In this case, Strike Zone Bowling is the better deal.
Therefore, bowling at Strike Zone would be a better deal than Fun Time when bowling for 3 hours.