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 played.
Let F(x) represent the total cost at Fun Time Bowling.
Let S(x) represent the total cost at Strike Zone Bowling.
The system of equations representing each bowling alley's cost is:
For Fun Time Bowling:
F(x) = 3 + 9x
For Strike Zone Bowling:
S(x) = 5 + 8x
Part B)
To find when both bowling alleys will cost the same amount, we can set F(x) equal to S(x) and solve for x:
3 + 9x = 5 + 8x
To solve for x, we can subtract 8x from both sides of the equation:
3 + x = 5
Now, subtract 3 from both sides:
x = 2
Therefore, both bowling alleys will cost the same amount after playing for 2 hours.
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-intercept for Strike Zone Bowling is (0,5)
The y-intercepts of the graphs represents the total cost.
The rate of change for FunTime bowling is $8
The true statements are:
- The rate of change for each Bowling Alley represents the cost of bowling per hour
- The y-intercept for Strike Zone Bowling is (0,5)
- The y-intercepts of the graphs represents the total cost.
When would Bowling at Strike Zone be a better deal then Fun Time?(1 point)
Responses
1 hour
Never
2 hours
3 hours
To determine when bowling at Strike Zone would be a better deal than Fun Time, we can compare the total costs for each bowling alley at different time intervals.
Let's compare the costs for 1 hour, 2 hours, and 3 hours:
For Fun Time Bowling:
F(1) = 3 + 9(1) = $12
F(2) = 3 + 9(2) = $21
F(3) = 3 + 9(3) = $30
For Strike Zone Bowling:
S(1) = 5 + 8(1) = $13
S(2) = 5 + 8(2) = $21
S(3) = 5 + 8(3) = $29
As we can see, at all time intervals, the total cost of bowling at Fun Time is higher than the total cost of bowling at Strike Zone. Therefore, Strike Zone would be a better deal than Fun Time regardless of the duration.
So the answer is: Never.
You are planning an event for 100 people. You have a budget of $380 for dessert. Each slice of cake costs $3.00 and each slice of pie costs $5.00.
Write a system of equations to determine the number of slices of cake and pie you can buy.
(1 point)
Responses
x−3y=380
x+5y=100
x+y=100
3x+5y=380
x−y=380
3x−5y=380
3x+5y=100
x+y=380
Let's define the variables:
Let x represent the number of slices of cake.
Let y represent the number of slices of pie.
The system of equations representing the situation is:
Equation 1: x + y = 100
This equation represents the total number of slices of cake and pie purchased should add up to 100, which is the total number of people.
Equation 2: 3x + 5y = 380
This equation represents the total cost of the desserts, where each slice of cake costs $3 and each slice of pie costs $5, and the total budget is $380.
Therefore, the correct system of equations is:
x + y = 100
3x + 5y = 380
Use the elimination method to determine the number of cake slices you can purchase.
To determine the number of cake slices you can purchase using the elimination method, we can eliminate the variable "y" by multiplying both sides of Equation 1 by -5 to make the coefficients of "y" in both equations cancel each other out when added together:
Equation 1: x + y = 100 (multiply by -5)
Equation 2: 3x + 5y = 380
-5(x + y) = -5(100)
-5x - 5y = -500
Now, add this modified Equation 1 to Equation 2:
-5x - 5y + 3x + 5y = -500 + 380
-2x = -120
Divide both sides of this equation by -2:
-2x / -2 = -120 / -2
x = 60
Therefore, you can purchase 60 slices of cake.