A tennis club offers two payment options:

Option1: $35 monthly fee plus $4/hour for court rental
Option 2: No monthly fee but $6.50/hour for court rental.
Let x = hours per month of court rental time.
a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:
Option 1: C=_________________
Option 2: C=_________________
b) How many hours would you have to rent the court so that the monthly cost of option 1, is less than option 2. Set up an inequality and show your work algebraically using the information in part a.
Answer:
Show your work here:

so for part 1 would be C = 35 + 4

The amount he pays is a function of the number of hours he plays, you make no mention of that in your equation

for option 1, C1 = 35 + 4x

since he pays no monthly fee for option 2, wouldn't that equation be
C2 = 6.5x ???

b) just translate the English into math
"..monthly cost of option 1, is less than option 2."

35 + 4x < 6.5x

-2.5x < -35
x > 14

notice that for 14 hours the two costs would be the same , but for more than 14 hours option 1 would be cheaper

I came up with 14 < x

Ummmh?

Suppose I said 10 < 20
Could I say 20 > 10 ????

a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:

Option 1: C = 35 + 4x

Explanation: For Option 1, there is a monthly fee of $35 and an additional cost of $4 per hour of court rental.

Option 2: C = 6.50x

Explanation: For Option 2, there is no monthly fee, but there is a cost of $6.50 per hour of court rental.

b) To find out how many hours you would have to rent the court so that the monthly cost of option 1 is less than option 2, we need to compare the two equations and solve the inequality.

We want to find x such that C (Option 1) < C (Option 2). Substituting the equations from part a:

35 + 4x < 6.50x

Simplifying the equation:

35 < 6.50x - 4x
35 < 2.50x

Dividing both sides of the inequality by 2.50:

35/2.50 < x

Simplifying the left side:

14 < x

Therefore, you would have to rent the court for more than 14 hours per month for the monthly cost of Option 1 to be less than the monthly cost of Option 2.

And that's how you solve for the monthly cost and find the number of hours required for one option to be cheaper than the other!