1. Fun Time Bowling has a shoe rental fee of $3.00 and $9.00 per hour. Strike Zone Bowling has a shoe rental fee of $3.00 and $8.00 per hour.
PART A: Define the variables and write a system of equation to represent each bowling alley.
PART B: Use the substitution method to determine when both bowling alleys will cost the same amount.
2. When would bowling at Strike Zone be a better deal than at Fun Time.
a) 2 hours
b) 3 hours
c) 1 hour
d) never
PART A:
Let x be the number of hours bowled.
Let F(x) represent the cost of bowling at Fun Time.
So, F(x) = 3 + 9x.
Let S(x) represent the cost of bowling at Strike Zone.
So, S(x) = 3 + 8x.
PART B:
To determine when both bowling alleys will cost the same amount, we can set the two cost equations equal to each other and solve for x.
3 + 9x = 3 + 8x
Subtract 3 from both sides:
9x = 8x
Subtract 8x from both sides:
x = 0
So, both bowling alleys will cost the same amount when no time is bowled.
2. To determine when bowling at Strike Zone would be a better deal than at Fun Time, we can compare the costs for different durations of bowling.
a) For 2 hours:
F(2) = 3 + 9(2) = 3 + 18 = 21
S(2) = 3 + 8(2) = 3 + 16 = 19
Strike Zone would be a better deal since it costs $19 compared to $21 at Fun Time.
b) For 3 hours:
F(3) = 3 + 9(3) = 3 + 27 = 30
S(3) = 3 + 8(3) = 3 + 24 = 27
Strike Zone would be a better deal since it costs $27 compared to $30 at Fun Time.
c) For 1 hour:
F(1) = 3 + 9(1) = 3 + 9 = 12
S(1) = 3 + 8(1) = 3 + 8 = 11
Strike Zone would be a better deal since it costs $11 compared to $12 at Fun Time.
d) Never, since Strike Zone is always cheaper for any duration of bowling.
Can we simply use y as being the number of hours bowled. rather than F (x) and S (x) in the equation? Show your work
Yes, we can use y as the number of hours bowled instead of F(x) and S(x). Let's rewrite the equations using y:
For Fun Time Bowling:
Cost = $3.00 + $9.00 * y = 3 + 9y
For Strike Zone Bowling:
Cost = $3.00 + $8.00 * y = 3 + 8y
To determine when both bowling alleys will cost the same amount, we can set the two cost equations equal to each other and solve for y:
3 + 9y = 3 + 8y
Subtract 3 from both sides:
9y = 8y
Subtract 8y from both sides:
y = 0
So, both bowling alleys will cost the same amount when no time is bowled (y = 0).
To determine when bowling at Strike Zone would be a better deal than at Fun Time, we can compare the costs for different durations of bowling.
a) For 2 hours:
Cost at Fun Time = 3 + 9(2) = 3 + 18 = 21
Cost at Strike Zone = 3 + 8(2) = 3 + 16 = 19
Strike Zone would be a better deal since it costs $19 compared to $21 at Fun Time.
b) For 3 hours:
Cost at Fun Time = 3 + 9(3) = 3 + 27 = 30
Cost at Strike Zone = 3 + 8(3) = 3 + 24 = 27
Strike Zone would be a better deal since it costs $27 compared to $30 at Fun Time.
c) For 1 hour:
Cost at Fun Time = 3 + 9(1) = 3 + 9 = 12
Cost at Strike Zone = 3 + 8(1) = 3 + 8 = 11
Strike Zone would be a better deal since it costs $11 compared to $12 at Fun Time.
d) Strike Zone is always a better deal than Fun Time for any duration of bowling.